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Simplifying (2z + -7)(8 + -1z) = 0 Reorder the terms: (-7 + 2z)(8 + -1z) = 0 Multiply (-7 + 2z) * (8 + -1z) (-7(8 + -1z) + 2z * (8 + -1z)) = 0 ((8 * -7 + -1z * -7) + 2z * (8 + -1z)) = 0 ((-56 + 7z) + 2z * (8 + -1z)) = 0 (-56 + 7z + (8 * 2z + -1z * 2z)) = 0 (-56 + 7z + (16z + -2z2)) = 0 Combine like terms: 7z + 16z = 23z (-56 + 23z + -2z2) = 0 Solving -56 + 23z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + z)(7 + -2z) = 0Subproblem 1
Set the factor '(-8 + z)' equal to zero and attempt to solve: Simplifying -8 + z = 0 Solving -8 + z = 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 + z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z = 0 + 8 z = 0 + 8 Combine like terms: 0 + 8 = 8 z = 8 Simplifying z = 8Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Solution
z = {8, 3.5}
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