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Simplifying (2w + -5)(3w + 6) = 0 Reorder the terms: (-5 + 2w)(3w + 6) = 0 Reorder the terms: (-5 + 2w)(6 + 3w) = 0 Multiply (-5 + 2w) * (6 + 3w) (-5(6 + 3w) + 2w * (6 + 3w)) = 0 ((6 * -5 + 3w * -5) + 2w * (6 + 3w)) = 0 ((-30 + -15w) + 2w * (6 + 3w)) = 0 (-30 + -15w + (6 * 2w + 3w * 2w)) = 0 (-30 + -15w + (12w + 6w2)) = 0 Combine like terms: -15w + 12w = -3w (-30 + -3w + 6w2) = 0 Solving -30 + -3w + 6w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -1w + 2w2) = 0 Factor a trinomial. 3((-2 + -1w)(5 + -2w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 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 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 2
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {-2, 2.5}
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