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Simplifying (7w + 4)(4w + -12) = 0 Reorder the terms: (4 + 7w)(4w + -12) = 0 Reorder the terms: (4 + 7w)(-12 + 4w) = 0 Multiply (4 + 7w) * (-12 + 4w) (4(-12 + 4w) + 7w * (-12 + 4w)) = 0 ((-12 * 4 + 4w * 4) + 7w * (-12 + 4w)) = 0 ((-48 + 16w) + 7w * (-12 + 4w)) = 0 (-48 + 16w + (-12 * 7w + 4w * 7w)) = 0 (-48 + 16w + (-84w + 28w2)) = 0 Combine like terms: 16w + -84w = -68w (-48 + -68w + 28w2) = 0 Solving -48 + -68w + 28w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -17w + 7w2) = 0 Factor a trinomial. 4((-4 + -7w)(3 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -7w)' equal to zero and attempt to solve: Simplifying -4 + -7w = 0 Solving -4 + -7w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7w = 0 + 4 -7w = 0 + 4 Combine like terms: 0 + 4 = 4 -7w = 4 Divide each side by '-7'. w = -0.5714285714 Simplifying w = -0.5714285714Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {-0.5714285714, 3}
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