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Simplifying 0 = z2 + -7z + 12 Reorder the terms: 0 = 12 + -7z + z2 Solving 0 = 12 + -7z + z2 Solving for variable 'z'. Combine like terms: 0 + -12 = -12 -12 + 7z + -1z2 = 12 + -7z + z2 + -12 + 7z + -1z2 Reorder the terms: -12 + 7z + -1z2 = 12 + -12 + -7z + 7z + z2 + -1z2 Combine like terms: 12 + -12 = 0 -12 + 7z + -1z2 = 0 + -7z + 7z + z2 + -1z2 -12 + 7z + -1z2 = -7z + 7z + z2 + -1z2 Combine like terms: -7z + 7z = 0 -12 + 7z + -1z2 = 0 + z2 + -1z2 -12 + 7z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -12 + 7z + -1z2 = 0 Factor a trinomial. (-4 + z)(3 + -1z) = 0Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve: Simplifying -4 + z = 0 Solving -4 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + z = 0 + 4 z = 0 + 4 Combine like terms: 0 + 4 = 4 z = 4 Simplifying z = 4Subproblem 2
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 = 3Solution
z = {4, 3}
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