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Simplifying (9z + -18)(12z + 6) = 0 Reorder the terms: (-18 + 9z)(12z + 6) = 0 Reorder the terms: (-18 + 9z)(6 + 12z) = 0 Multiply (-18 + 9z) * (6 + 12z) (-18(6 + 12z) + 9z * (6 + 12z)) = 0 ((6 * -18 + 12z * -18) + 9z * (6 + 12z)) = 0 ((-108 + -216z) + 9z * (6 + 12z)) = 0 (-108 + -216z + (6 * 9z + 12z * 9z)) = 0 (-108 + -216z + (54z + 108z2)) = 0 Combine like terms: -216z + 54z = -162z (-108 + -162z + 108z2) = 0 Solving -108 + -162z + 108z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '54'. 54(-2 + -3z + 2z2) = 0 Factor a trinomial. 54((-1 + -2z)(2 + -1z)) = 0 Ignore the factor 54.Subproblem 1
Set the factor '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {-0.5, 2}
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