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Simplifying (3 + -1z)(3z + 4) = 0 Reorder the terms: (3 + -1z)(4 + 3z) = 0 Multiply (3 + -1z) * (4 + 3z) (3(4 + 3z) + -1z * (4 + 3z)) = 0 ((4 * 3 + 3z * 3) + -1z * (4 + 3z)) = 0 ((12 + 9z) + -1z * (4 + 3z)) = 0 (12 + 9z + (4 * -1z + 3z * -1z)) = 0 (12 + 9z + (-4z + -3z2)) = 0 Combine like terms: 9z + -4z = 5z (12 + 5z + -3z2) = 0 Solving 12 + 5z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -1z)(4 + 3z) = 0Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Subproblem 2
Set the factor '(4 + 3z)' equal to zero and attempt to solve: Simplifying 4 + 3z = 0 Solving 4 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3z = 0 + -4 3z = 0 + -4 Combine like terms: 0 + -4 = -4 3z = -4 Divide each side by '3'. z = -1.333333333 Simplifying z = -1.333333333Solution
z = {3, -1.333333333}
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