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Simplifying (4w + -3)(5w + 4) = 2w + -11 Reorder the terms: (-3 + 4w)(5w + 4) = 2w + -11 Reorder the terms: (-3 + 4w)(4 + 5w) = 2w + -11 Multiply (-3 + 4w) * (4 + 5w) (-3(4 + 5w) + 4w * (4 + 5w)) = 2w + -11 ((4 * -3 + 5w * -3) + 4w * (4 + 5w)) = 2w + -11 ((-12 + -15w) + 4w * (4 + 5w)) = 2w + -11 (-12 + -15w + (4 * 4w + 5w * 4w)) = 2w + -11 (-12 + -15w + (16w + 20w2)) = 2w + -11 Combine like terms: -15w + 16w = 1w (-12 + 1w + 20w2) = 2w + -11 Reorder the terms: -12 + 1w + 20w2 = -11 + 2w Solving -12 + 1w + 20w2 = -11 + 2w Solving for variable 'w'. Reorder the terms: -12 + 11 + 1w + -2w + 20w2 = -11 + 2w + 11 + -2w Combine like terms: -12 + 11 = -1 -1 + 1w + -2w + 20w2 = -11 + 2w + 11 + -2w Combine like terms: 1w + -2w = -1w -1 + -1w + 20w2 = -11 + 2w + 11 + -2w Reorder the terms: -1 + -1w + 20w2 = -11 + 11 + 2w + -2w Combine like terms: -11 + 11 = 0 -1 + -1w + 20w2 = 0 + 2w + -2w -1 + -1w + 20w2 = 2w + -2w Combine like terms: 2w + -2w = 0 -1 + -1w + 20w2 = 0 Factor a trinomial. (-1 + -5w)(1 + -4w) = 0Subproblem 1
Set the factor '(-1 + -5w)' equal to zero and attempt to solve: Simplifying -1 + -5w = 0 Solving -1 + -5w = 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 + -5w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5w = 0 + 1 -5w = 0 + 1 Combine like terms: 0 + 1 = 1 -5w = 1 Divide each side by '-5'. w = -0.2 Simplifying w = -0.2Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Solution
w = {-0.2, 0.25}
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