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Simplifying (6z + 7)(4z + 3) = 0 Reorder the terms: (7 + 6z)(4z + 3) = 0 Reorder the terms: (7 + 6z)(3 + 4z) = 0 Multiply (7 + 6z) * (3 + 4z) (7(3 + 4z) + 6z * (3 + 4z)) = 0 ((3 * 7 + 4z * 7) + 6z * (3 + 4z)) = 0 ((21 + 28z) + 6z * (3 + 4z)) = 0 (21 + 28z + (3 * 6z + 4z * 6z)) = 0 (21 + 28z + (18z + 24z2)) = 0 Combine like terms: 28z + 18z = 46z (21 + 46z + 24z2) = 0 Solving 21 + 46z + 24z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + 6z)(3 + 4z) = 0Subproblem 1
Set the factor '(7 + 6z)' equal to zero and attempt to solve: Simplifying 7 + 6z = 0 Solving 7 + 6z = 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 + 6z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6z = 0 + -7 6z = 0 + -7 Combine like terms: 0 + -7 = -7 6z = -7 Divide each side by '6'. z = -1.166666667 Simplifying z = -1.166666667Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {-1.166666667, -0.75}
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