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Simplifying (8 + z)(4z + -6) = 0 Reorder the terms: (8 + z)(-6 + 4z) = 0 Multiply (8 + z) * (-6 + 4z) (8(-6 + 4z) + z(-6 + 4z)) = 0 ((-6 * 8 + 4z * 8) + z(-6 + 4z)) = 0 ((-48 + 32z) + z(-6 + 4z)) = 0 (-48 + 32z + (-6 * z + 4z * z)) = 0 (-48 + 32z + (-6z + 4z2)) = 0 Combine like terms: 32z + -6z = 26z (-48 + 26z + 4z2) = 0 Solving -48 + 26z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 13z + 2z2) = 0 Factor a trinomial. 2((-8 + -1z)(3 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8Subproblem 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 = {-8, 1.5}
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