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Simplifying 2z(3z + 1) = -9z + -3 Reorder the terms: 2z(1 + 3z) = -9z + -3 (1 * 2z + 3z * 2z) = -9z + -3 (2z + 6z2) = -9z + -3 Reorder the terms: 2z + 6z2 = -3 + -9z Solving 2z + 6z2 = -3 + -9z Solving for variable 'z'. Reorder the terms: 3 + 2z + 9z + 6z2 = -3 + -9z + 3 + 9z Combine like terms: 2z + 9z = 11z 3 + 11z + 6z2 = -3 + -9z + 3 + 9z Reorder the terms: 3 + 11z + 6z2 = -3 + 3 + -9z + 9z Combine like terms: -3 + 3 = 0 3 + 11z + 6z2 = 0 + -9z + 9z 3 + 11z + 6z2 = -9z + 9z Combine like terms: -9z + 9z = 0 3 + 11z + 6z2 = 0 Factor a trinomial. (3 + 2z)(1 + 3z) = 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 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {-1.5, -0.3333333333}
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