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Simplifying z2 = 45 + 12z Solving z2 = 45 + 12z Solving for variable 'z'. Reorder the terms: -45 + -12z + z2 = 45 + 12z + -45 + -12z Reorder the terms: -45 + -12z + z2 = 45 + -45 + 12z + -12z Combine like terms: 45 + -45 = 0 -45 + -12z + z2 = 0 + 12z + -12z -45 + -12z + z2 = 12z + -12z Combine like terms: 12z + -12z = 0 -45 + -12z + z2 = 0 Factor a trinomial. (-3 + -1z)(15 + -1z) = 0Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 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 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 2
Set the factor '(15 + -1z)' equal to zero and attempt to solve: Simplifying 15 + -1z = 0 Solving 15 + -1z = 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 + -1z = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1z = 0 + -15 -1z = 0 + -15 Combine like terms: 0 + -15 = -15 -1z = -15 Divide each side by '-1'. z = 15 Simplifying z = 15Solution
z = {-3, 15}
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