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Simplifying 8z2 + 7z + 10 = 7z2 + 17z + -6 Reorder the terms: 10 + 7z + 8z2 = 7z2 + 17z + -6 Reorder the terms: 10 + 7z + 8z2 = -6 + 17z + 7z2 Solving 10 + 7z + 8z2 = -6 + 17z + 7z2 Solving for variable 'z'. Reorder the terms: 10 + 6 + 7z + -17z + 8z2 + -7z2 = -6 + 17z + 7z2 + 6 + -17z + -7z2 Combine like terms: 10 + 6 = 16 16 + 7z + -17z + 8z2 + -7z2 = -6 + 17z + 7z2 + 6 + -17z + -7z2 Combine like terms: 7z + -17z = -10z 16 + -10z + 8z2 + -7z2 = -6 + 17z + 7z2 + 6 + -17z + -7z2 Combine like terms: 8z2 + -7z2 = 1z2 16 + -10z + 1z2 = -6 + 17z + 7z2 + 6 + -17z + -7z2 Reorder the terms: 16 + -10z + 1z2 = -6 + 6 + 17z + -17z + 7z2 + -7z2 Combine like terms: -6 + 6 = 0 16 + -10z + 1z2 = 0 + 17z + -17z + 7z2 + -7z2 16 + -10z + 1z2 = 17z + -17z + 7z2 + -7z2 Combine like terms: 17z + -17z = 0 16 + -10z + 1z2 = 0 + 7z2 + -7z2 16 + -10z + 1z2 = 7z2 + -7z2 Combine like terms: 7z2 + -7z2 = 0 16 + -10z + 1z2 = 0 Factor a trinomial. (2 + -1z)(8 + -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 '(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 = {2, 8}
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