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Simplifying 4z(2z + 3) = 6z + 9 Reorder the terms: 4z(3 + 2z) = 6z + 9 (3 * 4z + 2z * 4z) = 6z + 9 (12z + 8z2) = 6z + 9 Reorder the terms: 12z + 8z2 = 9 + 6z Solving 12z + 8z2 = 9 + 6z Solving for variable 'z'. Reorder the terms: -9 + 12z + -6z + 8z2 = 9 + 6z + -9 + -6z Combine like terms: 12z + -6z = 6z -9 + 6z + 8z2 = 9 + 6z + -9 + -6z Reorder the terms: -9 + 6z + 8z2 = 9 + -9 + 6z + -6z Combine like terms: 9 + -9 = 0 -9 + 6z + 8z2 = 0 + 6z + -6z -9 + 6z + 8z2 = 6z + -6z Combine like terms: 6z + -6z = 0 -9 + 6z + 8z2 = 0 Factor a trinomial. (-3 + -2z)(3 + -4z) = 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 '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {-1.5, 0.75}
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