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Simplifying (3z + -2)(9 + z) = 0 Reorder the terms: (-2 + 3z)(9 + z) = 0 Multiply (-2 + 3z) * (9 + z) (-2(9 + z) + 3z * (9 + z)) = 0 ((9 * -2 + z * -2) + 3z * (9 + z)) = 0 ((-18 + -2z) + 3z * (9 + z)) = 0 (-18 + -2z + (9 * 3z + z * 3z)) = 0 (-18 + -2z + (27z + 3z2)) = 0 Combine like terms: -2z + 27z = 25z (-18 + 25z + 3z2) = 0 Solving -18 + 25z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(2 + -3z) = 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 '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {-9, 0.6666666667}
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