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Simplifying (2z + -3)(9 + z) = 0 Reorder the terms: (-3 + 2z)(9 + z) = 0 Multiply (-3 + 2z) * (9 + z) (-3(9 + z) + 2z * (9 + z)) = 0 ((9 * -3 + z * -3) + 2z * (9 + z)) = 0 ((-27 + -3z) + 2z * (9 + z)) = 0 (-27 + -3z + (9 * 2z + z * 2z)) = 0 (-27 + -3z + (18z + 2z2)) = 0 Combine like terms: -3z + 18z = 15z (-27 + 15z + 2z2) = 0 Solving -27 + 15z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(3 + -2z) = 0Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9Subproblem 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 = {-9, 1.5}
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