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Simplifying 7z2 = 4 + -12z Solving 7z2 = 4 + -12z Solving for variable 'z'. Reorder the terms: -4 + 12z + 7z2 = 4 + -12z + -4 + 12z Reorder the terms: -4 + 12z + 7z2 = 4 + -4 + -12z + 12z Combine like terms: 4 + -4 = 0 -4 + 12z + 7z2 = 0 + -12z + 12z -4 + 12z + 7z2 = -12z + 12z Combine like terms: -12z + 12z = 0 -4 + 12z + 7z2 = 0 Factor a trinomial. (-2 + -1z)(2 + -7z) = 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 '(2 + -7z)' equal to zero and attempt to solve: Simplifying 2 + -7z = 0 Solving 2 + -7z = 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 + -7z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7z = 0 + -2 -7z = 0 + -2 Combine like terms: 0 + -2 = -2 -7z = -2 Divide each side by '-7'. z = 0.2857142857 Simplifying z = 0.2857142857Solution
z = {-2, 0.2857142857}
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