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Simplifying 6w2 = 16 + 20w Solving 6w2 = 16 + 20w Solving for variable 'w'. Reorder the terms: -16 + -20w + 6w2 = 16 + 20w + -16 + -20w Reorder the terms: -16 + -20w + 6w2 = 16 + -16 + 20w + -20w Combine like terms: 16 + -16 = 0 -16 + -20w + 6w2 = 0 + 20w + -20w -16 + -20w + 6w2 = 20w + -20w Combine like terms: 20w + -20w = 0 -16 + -20w + 6w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -10w + 3w2) = 0 Factor a trinomial. 2((-2 + -3w)(4 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -3w)' equal to zero and attempt to solve: Simplifying -2 + -3w = 0 Solving -2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3w = 0 + 2 -3w = 0 + 2 Combine like terms: 0 + 2 = 2 -3w = 2 Divide each side by '-3'. w = -0.6666666667 Simplifying w = -0.6666666667Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-0.6666666667, 4}
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