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Simplifying 5w(-3w2 + 2w + -4) = 0 Reorder the terms: 5w(-4 + 2w + -3w2) = 0 (-4 * 5w + 2w * 5w + -3w2 * 5w) = 0 (-20w + 10w2 + -15w3) = 0 Solving -20w + 10w2 + -15w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(-4 + 2w + -3w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-4 + 2w + -3w2)' equal to zero and attempt to solve: Simplifying -4 + 2w + -3w2 = 0 Solving -4 + 2w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -0.6666666667w + -1.333333333 + w2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -0.6666666667w + w2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -0.6666666667w + w2 = 0 + -1.333333333 -0.6666666667w + w2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -0.6666666667w + w2 = -1.333333333 The w term is -0.6666666667w. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667w + 0.1111111112 + w2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + -0.6666666667w + w2 = -1.2222222218 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = -1.2222222218 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
w = {0}
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