3w^2=15w

{ "query": { "display": "$$3w^{2}=15w$$", "symbolab_question": "EQUATION#3w^{2}=15w" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Equations", "subTopic": "Quadratic", "default": "w=0,w=5", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$3w^{2}=15w{\\quad:\\quad}w=0,\\:w=5$$", "input": "3w^{2}=15w", "steps": [ { "type": "interim", "title": "Desplace $$15w\\:$$a la izquierda", "input": "3w^{2}=15w", "result": "3w^{2}-15w=0", "steps": [ { "type": "step", "primary": "Restar $$15w$$ de ambos lados", "result": "3w^{2}-15w=15w-15w" }, { "type": "step", "primary": "Simplificar", "result": "3w^{2}-15w=0" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Factorizar $$3w^{2}-15w:{\\quad}3w\\left(w-5\\right)$$", "input": "3w^{2}-15w", "steps": [ { "type": "step", "primary": "Aplicar las leyes de los exponentes: $$a^{b+c}=a^{b}a^{c}$$", "secondary": [ "$$w^{2}=ww$$" ], "result": "=3ww-15w", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Reescribir $$15$$ como $$3\\cdot\\:5$$", "result": "=3ww-3\\cdot\\:5w" }, { "type": "step", "primary": "Factorizar el termino común $$3w$$", "result": "=3w\\left(w-5\\right)", "meta": { "practiceLink": "/practice/factoring-practice", "practiceTopic": "Factoring" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Factor Specific 1Eq" } }, { "type": "step", "result": "3w\\left(w-5\\right)=0" }, { "type": "step", "primary": "Usando la propiedad del factor cero:$$\\quad$$ Si $$ab=0\\:$$entonces $$a=0\\:$$o $$b=0$$", "result": "w=0\\lor\\:w-5=0" }, { "type": "interim", "title": "Resolver $$w-5=0:{\\quad}w=5$$", "input": "w-5=0", "steps": [ { "type": "interim", "title": "Desplace $$5\\:$$a la derecha", "input": "w-5=0", "result": "w=5", "steps": [ { "type": "step", "primary": "Sumar $$5$$ a ambos lados", "result": "w-5+5=0+5" }, { "type": "step", "primary": "Simplificar", "result": "w=5" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7zJoXncAnwIJ4jzzANcIUNJN1pXT08zEQpn0WJ6CFMXAJvCA6oISTy39okC4yj2qzPlRMTLc8dpF+T7mmaRQSVuuBpdpGUoF4uq9RVaaUScmsHuCWujTcybm8y4lstc3AiiuTvHZMNMidREaJCrkWGaF1k4VM3a1qkR3oJq1IGYTLfCE3WGmRo856cutzgvhPRTITn0EwTWnWxh77Pke2Jktw+A4ntMAfEpQrL9q+dyUVk8t2Twjh+zjp9dlYTco/GgwSbIcd5JjP/d1KuCbW94zDSf2vh/i+3s4cO/oKwZy1rKw+72V41LgxeCOecKXOfIvtRFItCUfO72DblJDvr6ag359nJICSNxR1sdkiJYDwt9LEn7QCBUukJKctfSJKF8odSqXg564E4E1b37wWvvFEB2FLwTBz/MhDswS14YiS3hSct2H0MPXtovfRuE4G" } } ], "meta": { "solvingClass": "Equations", "interimType": "Generic Solve Title 1Eq" } }, { "type": "step", "primary": "Las soluciones a la ecuación de segundo grado son: ", "result": "w=0,\\:w=5" } ], "meta": { "solvingClass": "Equations", "practiceLink": "/practice/quadratic-equations-practice", "practiceTopic": "Quadratic Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "w", "plotRequest": "3w^{2}-15w" }, "showViewLarger": true } }, "meta": { "showVerify": true } }