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Simplifying (8 + z)(4z + 7) = 0 Reorder the terms: (8 + z)(7 + 4z) = 0 Multiply (8 + z) * (7 + 4z) (8(7 + 4z) + z(7 + 4z)) = 0 ((7 * 8 + 4z * 8) + z(7 + 4z)) = 0 ((56 + 32z) + z(7 + 4z)) = 0 (56 + 32z + (7 * z + 4z * z)) = 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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