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Simplifying (8 + -1z)(4z + -3) = 0 Reorder the terms: (8 + -1z)(-3 + 4z) = 0 Multiply (8 + -1z) * (-3 + 4z) (8(-3 + 4z) + -1z * (-3 + 4z)) = 0 ((-3 * 8 + 4z * 8) + -1z * (-3 + 4z)) = 0 ((-24 + 32z) + -1z * (-3 + 4z)) = 0 (-24 + 32z + (-3 * -1z + 4z * -1z)) = 0 (-24 + 32z + (3z + -4z2)) = 0 Combine like terms: 32z + 3z = 35z (-24 + 35z + -4z2) = 0 Solving -24 + 35z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + z)(3 + -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 '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {8, 0.75}
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