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Simplifying (2w + 4)(5w + 1) = 13w + 13 Reorder the terms: (4 + 2w)(5w + 1) = 13w + 13 Reorder the terms: (4 + 2w)(1 + 5w) = 13w + 13 Multiply (4 + 2w) * (1 + 5w) (4(1 + 5w) + 2w * (1 + 5w)) = 13w + 13 ((1 * 4 + 5w * 4) + 2w * (1 + 5w)) = 13w + 13 ((4 + 20w) + 2w * (1 + 5w)) = 13w + 13 (4 + 20w + (1 * 2w + 5w * 2w)) = 13w + 13 (4 + 20w + (2w + 10w2)) = 13w + 13 Combine like terms: 20w + 2w = 22w (4 + 22w + 10w2) = 13w + 13 Reorder the terms: 4 + 22w + 10w2 = 13 + 13w Solving 4 + 22w + 10w2 = 13 + 13w Solving for variable 'w'. Reorder the terms: 4 + -13 + 22w + -13w + 10w2 = 13 + 13w + -13 + -13w Combine like terms: 4 + -13 = -9 -9 + 22w + -13w + 10w2 = 13 + 13w + -13 + -13w Combine like terms: 22w + -13w = 9w -9 + 9w + 10w2 = 13 + 13w + -13 + -13w Reorder the terms: -9 + 9w + 10w2 = 13 + -13 + 13w + -13w Combine like terms: 13 + -13 = 0 -9 + 9w + 10w2 = 0 + 13w + -13w -9 + 9w + 10w2 = 13w + -13w Combine like terms: 13w + -13w = 0 -9 + 9w + 10w2 = 0 Factor a trinomial. (-3 + -2w)(3 + -5w) = 0Subproblem 1
Set the factor '(-3 + -2w)' equal to zero and attempt to solve: Simplifying -3 + -2w = 0 Solving -3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2w = 0 + 3 -2w = 0 + 3 Combine like terms: 0 + 3 = 3 -2w = 3 Divide each side by '-2'. w = -1.5 Simplifying w = -1.5Subproblem 2
Set the factor '(3 + -5w)' equal to zero and attempt to solve: Simplifying 3 + -5w = 0 Solving 3 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5w = 0 + -3 -5w = 0 + -3 Combine like terms: 0 + -3 = -3 -5w = -3 Divide each side by '-5'. w = 0.6 Simplifying w = 0.6Solution
w = {-1.5, 0.6}
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