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Simplifying (4z + 6)(7 + z) = 0 Reorder the terms: (6 + 4z)(7 + z) = 0 Multiply (6 + 4z) * (7 + z) (6(7 + z) + 4z * (7 + z)) = 0 ((7 * 6 + z * 6) + 4z * (7 + z)) = 0 ((42 + 6z) + 4z * (7 + z)) = 0 (42 + 6z + (7 * 4z + z * 4z)) = 0 (42 + 6z + (28z + 4z2)) = 0 Combine like terms: 6z + 28z = 34z (42 + 34z + 4z2) = 0 Solving 42 + 34z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 17z + 2z2) = 0 Factor a trinomial. 2((7 + z)(3 + 2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 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 = {-7, -1.5}
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