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Simplifying 2w(3w + -2) = -3w + 2 Reorder the terms: 2w(-2 + 3w) = -3w + 2 (-2 * 2w + 3w * 2w) = -3w + 2 (-4w + 6w2) = -3w + 2 Reorder the terms: -4w + 6w2 = 2 + -3w Solving -4w + 6w2 = 2 + -3w Solving for variable 'w'. Reorder the terms: -2 + -4w + 3w + 6w2 = 2 + -3w + -2 + 3w Combine like terms: -4w + 3w = -1w -2 + -1w + 6w2 = 2 + -3w + -2 + 3w Reorder the terms: -2 + -1w + 6w2 = 2 + -2 + -3w + 3w Combine like terms: 2 + -2 = 0 -2 + -1w + 6w2 = 0 + -3w + 3w -2 + -1w + 6w2 = -3w + 3w Combine like terms: -3w + 3w = 0 -2 + -1w + 6w2 = 0 Factor a trinomial. (-1 + -2w)(2 + -3w) = 0Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 2
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 = 0.6666666667Solution
w = {-0.5, 0.6666666667}
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