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Simplifying z2 = 3z + 40 Reorder the terms: z2 = 40 + 3z Solving z2 = 40 + 3z Solving for variable 'z'. Reorder the terms: -40 + -3z + z2 = 40 + 3z + -40 + -3z Reorder the terms: -40 + -3z + z2 = 40 + -40 + 3z + -3z Combine like terms: 40 + -40 = 0 -40 + -3z + z2 = 0 + 3z + -3z -40 + -3z + z2 = 3z + -3z Combine like terms: 3z + -3z = 0 -40 + -3z + z2 = 0 Factor a trinomial. (-5 + -1z)(8 + -1z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {-5, 8}
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