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Simplifying 9z2 = 6z + 15 Reorder the terms: 9z2 = 15 + 6z Solving 9z2 = 15 + 6z Solving for variable 'z'. Reorder the terms: -15 + -6z + 9z2 = 15 + 6z + -15 + -6z Reorder the terms: -15 + -6z + 9z2 = 15 + -15 + 6z + -6z Combine like terms: 15 + -15 = 0 -15 + -6z + 9z2 = 0 + 6z + -6z -15 + -6z + 9z2 = 6z + -6z Combine like terms: 6z + -6z = 0 -15 + -6z + 9z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -2z + 3z2) = 0 Factor a trinomial. 3((-1 + -1z)(5 + -3z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 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 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {-1, 1.666666667}
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