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Simplifying 3z(z + 4) = -1(z2 + 9) Reorder the terms: 3z(4 + z) = -1(z2 + 9) (4 * 3z + z * 3z) = -1(z2 + 9) (12z + 3z2) = -1(z2 + 9) Reorder the terms: 12z + 3z2 = -1(9 + z2) 12z + 3z2 = (9 * -1 + z2 * -1) 12z + 3z2 = (-9 + -1z2) Solving 12z + 3z2 = -9 + -1z2 Solving for variable 'z'. Reorder the terms: 9 + 12z + 3z2 + z2 = -9 + -1z2 + 9 + z2 Combine like terms: 3z2 + z2 = 4z2 9 + 12z + 4z2 = -9 + -1z2 + 9 + z2 Reorder the terms: 9 + 12z + 4z2 = -9 + 9 + -1z2 + z2 Combine like terms: -9 + 9 = 0 9 + 12z + 4z2 = 0 + -1z2 + z2 9 + 12z + 4z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 9 + 12z + 4z2 = 0 Factor a trinomial. (3 + 2z)(3 + 2z) = 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 + 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 = {-1.5, -1.5}
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