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Simplifying (8 + -1z)(4z + -7) = 0 Reorder the terms: (8 + -1z)(-7 + 4z) = 0 Multiply (8 + -1z) * (-7 + 4z) (8(-7 + 4z) + -1z * (-7 + 4z)) = 0 ((-7 * 8 + 4z * 8) + -1z * (-7 + 4z)) = 0 ((-56 + 32z) + -1z * (-7 + 4z)) = 0 (-56 + 32z + (-7 * -1z + 4z * -1z)) = 0 (-56 + 32z + (7z + -4z2)) = 0 Combine like terms: 32z + 7z = 39z (-56 + 39z + -4z2) = 0 Solving -56 + 39z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + z)(7 + -4z) = 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 + -4z)' equal to zero and attempt to solve: Simplifying 7 + -4z = 0 Solving 7 + -4z = 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 + -4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4z = 0 + -7 -4z = 0 + -7 Combine like terms: 0 + -7 = -7 -4z = -7 Divide each side by '-4'. z = 1.75 Simplifying z = 1.75Solution
z = {8, 1.75}
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