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Simplifying (2z + 3)(4 + -1z) = 0 Reorder the terms: (3 + 2z)(4 + -1z) = 0 Multiply (3 + 2z) * (4 + -1z) (3(4 + -1z) + 2z * (4 + -1z)) = 0 ((4 * 3 + -1z * 3) + 2z * (4 + -1z)) = 0 ((12 + -3z) + 2z * (4 + -1z)) = 0 (12 + -3z + (4 * 2z + -1z * 2z)) = 0 (12 + -3z + (8z + -2z2)) = 0 Combine like terms: -3z + 8z = 5z (12 + 5z + -2z2) = 0 Solving 12 + 5z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(3 + 2z) = 0Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Subproblem 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 = {4, -1.5}
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