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Simplifying (9 + z)(4z + -2) = 0 Reorder the terms: (9 + z)(-2 + 4z) = 0 Multiply (9 + z) * (-2 + 4z) (9(-2 + 4z) + z(-2 + 4z)) = 0 ((-2 * 9 + 4z * 9) + z(-2 + 4z)) = 0 ((-18 + 36z) + z(-2 + 4z)) = 0 (-18 + 36z + (-2 * z + 4z * z)) = 0 (-18 + 36z + (-2z + 4z2)) = 0 Combine like terms: 36z + -2z = 34z (-18 + 34z + 4z2) = 0 Solving -18 + 34z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 17z + 2z2) = 0 Factor a trinomial. 2((-9 + -1z)(1 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9Subproblem 2
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 = 0.5Solution
z = {-9, 0.5}
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