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Simplifying (4z + 12)(14 + -7z) = 0 Reorder the terms: (12 + 4z)(14 + -7z) = 0 Multiply (12 + 4z) * (14 + -7z) (12(14 + -7z) + 4z * (14 + -7z)) = 0 ((14 * 12 + -7z * 12) + 4z * (14 + -7z)) = 0 ((168 + -84z) + 4z * (14 + -7z)) = 0 (168 + -84z + (14 * 4z + -7z * 4z)) = 0 (168 + -84z + (56z + -28z2)) = 0 Combine like terms: -84z + 56z = -28z (168 + -28z + -28z2) = 0 Solving 168 + -28z + -28z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '28'. 28(6 + -1z + -1z2) = 0 Factor a trinomial. 28((2 + -1z)(3 + z)) = 0 Ignore the factor 28.Subproblem 1
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 = 2Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 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 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Solution
z = {2, -3}
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