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Simplifying (5z + 2)(8 + z) = 0 Reorder the terms: (2 + 5z)(8 + z) = 0 Multiply (2 + 5z) * (8 + z) (2(8 + z) + 5z * (8 + z)) = 0 ((8 * 2 + z * 2) + 5z * (8 + z)) = 0 ((16 + 2z) + 5z * (8 + z)) = 0 (16 + 2z + (8 * 5z + z * 5z)) = 0 (16 + 2z + (40z + 5z2)) = 0 Combine like terms: 2z + 40z = 42z (16 + 42z + 5z2) = 0 Solving 16 + 42z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (8 + z)(2 + 5z) = 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 '(2 + 5z)' equal to zero and attempt to solve: Simplifying 2 + 5z = 0 Solving 2 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5z = 0 + -2 5z = 0 + -2 Combine like terms: 0 + -2 = -2 5z = -2 Divide each side by '5'. z = -0.4 Simplifying z = -0.4Solution
z = {-8, -0.4}
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