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Simplifying 2z2 + 3z = 135 Reorder the terms: 3z + 2z2 = 135 Solving 3z + 2z2 = 135 Solving for variable 'z'. Reorder the terms: -135 + 3z + 2z2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + 3z + 2z2 = 0 Factor a trinomial. (-9 + -1z)(15 + -2z) = 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 '(15 + -2z)' equal to zero and attempt to solve: Simplifying 15 + -2z = 0 Solving 15 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2z = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2z = 0 + -15 -2z = 0 + -15 Combine like terms: 0 + -15 = -15 -2z = -15 Divide each side by '-2'. z = 7.5 Simplifying z = 7.5Solution
z = {-9, 7.5}
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