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Simplifying (5w + -5)(3w + 3) = 1w + -13 Reorder the terms: (-5 + 5w)(3w + 3) = 1w + -13 Reorder the terms: (-5 + 5w)(3 + 3w) = 1w + -13 Multiply (-5 + 5w) * (3 + 3w) (-5(3 + 3w) + 5w * (3 + 3w)) = 1w + -13 ((3 * -5 + 3w * -5) + 5w * (3 + 3w)) = 1w + -13 ((-15 + -15w) + 5w * (3 + 3w)) = 1w + -13 (-15 + -15w + (3 * 5w + 3w * 5w)) = 1w + -13 (-15 + -15w + (15w + 15w2)) = 1w + -13 Combine like terms: -15w + 15w = 0 (-15 + 0 + 15w2) = 1w + -13 (-15 + 15w2) = 1w + -13 Reorder the terms: -15 + 15w2 = -13 + 1w Solving -15 + 15w2 = -13 + 1w Solving for variable 'w'. Reorder the terms: -15 + 13 + -1w + 15w2 = -13 + 1w + 13 + -1w Combine like terms: -15 + 13 = -2 -2 + -1w + 15w2 = -13 + 1w + 13 + -1w Reorder the terms: -2 + -1w + 15w2 = -13 + 13 + 1w + -1w Combine like terms: -13 + 13 = 0 -2 + -1w + 15w2 = 0 + 1w + -1w -2 + -1w + 15w2 = 1w + -1w Combine like terms: 1w + -1w = 0 -2 + -1w + 15w2 = 0 Factor a trinomial. (-1 + -3w)(2 + -5w) = 0Subproblem 1
Set the factor '(-1 + -3w)' equal to zero and attempt to solve: Simplifying -1 + -3w = 0 Solving -1 + -3w = 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 + -3w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3w = 0 + 1 -3w = 0 + 1 Combine like terms: 0 + 1 = 1 -3w = 1 Divide each side by '-3'. w = -0.3333333333 Simplifying w = -0.3333333333Subproblem 2
Set the factor '(2 + -5w)' equal to zero and attempt to solve: Simplifying 2 + -5w = 0 Solving 2 + -5w = 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 + -5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5w = 0 + -2 -5w = 0 + -2 Combine like terms: 0 + -2 = -2 -5w = -2 Divide each side by '-5'. w = 0.4 Simplifying w = 0.4Solution
w = {-0.3333333333, 0.4}
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