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Simplifying -4(z + 6)(-1z + 2) = 0 Reorder the terms: -4(6 + z)(-1z + 2) = 0 Reorder the terms: -4(6 + z)(2 + -1z) = 0 Multiply (6 + z) * (2 + -1z) -4(6(2 + -1z) + z(2 + -1z)) = 0 -4((2 * 6 + -1z * 6) + z(2 + -1z)) = 0 -4((12 + -6z) + z(2 + -1z)) = 0 -4(12 + -6z + (2 * z + -1z * z)) = 0 -4(12 + -6z + (2z + -1z2)) = 0 Combine like terms: -6z + 2z = -4z -4(12 + -4z + -1z2) = 0 (12 * -4 + -4z * -4 + -1z2 * -4) = 0 (-48 + 16z + 4z2) = 0 Solving -48 + 16z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + 4z + z2) = 0 Factor a trinomial. 4((-6 + -1z)(2 + -1z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 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 = {-6, 2}
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