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Simplifying (w + 2)(w + -2) + (6w + 5)(w + -2) = 0 Reorder the terms: (2 + w)(w + -2) + (6w + 5)(w + -2) = 0 Reorder the terms: (2 + w)(-2 + w) + (6w + 5)(w + -2) = 0 Multiply (2 + w) * (-2 + w) (2(-2 + w) + w(-2 + w)) + (6w + 5)(w + -2) = 0 ((-2 * 2 + w * 2) + w(-2 + w)) + (6w + 5)(w + -2) = 0 ((-4 + 2w) + w(-2 + w)) + (6w + 5)(w + -2) = 0 (-4 + 2w + (-2 * w + w * w)) + (6w + 5)(w + -2) = 0 (-4 + 2w + (-2w + w2)) + (6w + 5)(w + -2) = 0 Combine like terms: 2w + -2w = 0 (-4 + 0 + w2) + (6w + 5)(w + -2) = 0 (-4 + w2) + (6w + 5)(w + -2) = 0 Reorder the terms: -4 + w2 + (5 + 6w)(w + -2) = 0 Reorder the terms: -4 + w2 + (5 + 6w)(-2 + w) = 0 Multiply (5 + 6w) * (-2 + w) -4 + w2 + (5(-2 + w) + 6w * (-2 + w)) = 0 -4 + w2 + ((-2 * 5 + w * 5) + 6w * (-2 + w)) = 0 -4 + w2 + ((-10 + 5w) + 6w * (-2 + w)) = 0 -4 + w2 + (-10 + 5w + (-2 * 6w + w * 6w)) = 0 -4 + w2 + (-10 + 5w + (-12w + 6w2)) = 0 Combine like terms: 5w + -12w = -7w -4 + w2 + (-10 + -7w + 6w2) = 0 Reorder the terms: -4 + -10 + -7w + w2 + 6w2 = 0 Combine like terms: -4 + -10 = -14 -14 + -7w + w2 + 6w2 = 0 Combine like terms: w2 + 6w2 = 7w2 -14 + -7w + 7w2 = 0 Solving -14 + -7w + 7w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + -1w + w2) = 0 Factor a trinomial. 7((-1 + -1w)(2 + -1w)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 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 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
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 = 2Solution
w = {-1, 2}
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