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Simplifying z2 + 2 = 12 + 3z Reorder the terms: 2 + z2 = 12 + 3z Solving 2 + z2 = 12 + 3z Solving for variable 'z'. Reorder the terms: 2 + -12 + -3z + z2 = 12 + 3z + -12 + -3z Combine like terms: 2 + -12 = -10 -10 + -3z + z2 = 12 + 3z + -12 + -3z Reorder the terms: -10 + -3z + z2 = 12 + -12 + 3z + -3z Combine like terms: 12 + -12 = 0 -10 + -3z + z2 = 0 + 3z + -3z -10 + -3z + z2 = 3z + -3z Combine like terms: 3z + -3z = 0 -10 + -3z + z2 = 0 Factor a trinomial. (-2 + -1z)(5 + -1z) = 0Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 2
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 = 5Solution
z = {-2, 5}
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