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Simplifying (w + -8)(2w + 10) = 0 Reorder the terms: (-8 + w)(2w + 10) = 0 Reorder the terms: (-8 + w)(10 + 2w) = 0 Multiply (-8 + w) * (10 + 2w) (-8(10 + 2w) + w(10 + 2w)) = 0 ((10 * -8 + 2w * -8) + w(10 + 2w)) = 0 ((-80 + -16w) + w(10 + 2w)) = 0 (-80 + -16w + (10 * w + 2w * w)) = 0 (-80 + -16w + (10w + 2w2)) = 0 Combine like terms: -16w + 10w = -6w (-80 + -6w + 2w2) = 0 Solving -80 + -6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -3w + w2) = 0 Factor a trinomial. 2((-5 + -1w)(8 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-5, 8}
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