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Simplifying (5z + 4)(1 + z) = 0 Reorder the terms: (4 + 5z)(1 + z) = 0 Multiply (4 + 5z) * (1 + z) (4(1 + z) + 5z * (1 + z)) = 0 ((1 * 4 + z * 4) + 5z * (1 + z)) = 0 ((4 + 4z) + 5z * (1 + z)) = 0 (4 + 4z + (1 * 5z + z * 5z)) = 0 (4 + 4z + (5z + 5z2)) = 0 Combine like terms: 4z + 5z = 9z (4 + 9z + 5z2) = 0 Solving 4 + 9z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + z)(4 + 5z) = 0Subproblem 1
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 2
Set the factor '(4 + 5z)' equal to zero and attempt to solve: Simplifying 4 + 5z = 0 Solving 4 + 5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5z = 0 + -4 5z = 0 + -4 Combine like terms: 0 + -4 = -4 5z = -4 Divide each side by '5'. z = -0.8 Simplifying z = -0.8Solution
z = {-1, -0.8}
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