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Simplifying (2z + 3)(1 + z) = 0 Reorder the terms: (3 + 2z)(1 + z) = 0 Multiply (3 + 2z) * (1 + z) (3(1 + z) + 2z * (1 + z)) = 0 ((1 * 3 + z * 3) + 2z * (1 + z)) = 0 ((3 + 3z) + 2z * (1 + z)) = 0 (3 + 3z + (1 * 2z + z * 2z)) = 0 (3 + 3z + (2z + 2z2)) = 0 Combine like terms: 3z + 2z = 5z (3 + 5z + 2z2) = 0 Solving 3 + 5z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + 2z)(1 + z) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {-1.5, -1}
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