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Simplifying (5z + 3)(8 + -1z) = 0 Reorder the terms: (3 + 5z)(8 + -1z) = 0 Multiply (3 + 5z) * (8 + -1z) (3(8 + -1z) + 5z * (8 + -1z)) = 0 ((8 * 3 + -1z * 3) + 5z * (8 + -1z)) = 0 ((24 + -3z) + 5z * (8 + -1z)) = 0 (24 + -3z + (8 * 5z + -1z * 5z)) = 0 (24 + -3z + (40z + -5z2)) = 0 Combine like terms: -3z + 40z = 37z (24 + 37z + -5z2) = 0 Solving 24 + 37z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + -1z)(3 + 5z) = 0Subproblem 1
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 = 8Subproblem 2
Set the factor '(3 + 5z)' equal to zero and attempt to solve: Simplifying 3 + 5z = 0 Solving 3 + 5z = 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 + 5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5z = 0 + -3 5z = 0 + -3 Combine like terms: 0 + -3 = -3 5z = -3 Divide each side by '5'. z = -0.6 Simplifying z = -0.6Solution
z = {8, -0.6}
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