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Simplifying (4z + -6)(9 + -1z) = 0 Reorder the terms: (-6 + 4z)(9 + -1z) = 0 Multiply (-6 + 4z) * (9 + -1z) (-6(9 + -1z) + 4z * (9 + -1z)) = 0 ((9 * -6 + -1z * -6) + 4z * (9 + -1z)) = 0 ((-54 + 6z) + 4z * (9 + -1z)) = 0 (-54 + 6z + (9 * 4z + -1z * 4z)) = 0 (-54 + 6z + (36z + -4z2)) = 0 Combine like terms: 6z + 36z = 42z (-54 + 42z + -4z2) = 0 Solving -54 + 42z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 21z + -2z2) = 0 Factor a trinomial. 2((-9 + z)(3 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 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 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {9, 1.5}
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