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Simplifying (4 + z)(5z + 2) = 0 Reorder the terms: (4 + z)(2 + 5z) = 0 Multiply (4 + z) * (2 + 5z) (4(2 + 5z) + z(2 + 5z)) = 0 ((2 * 4 + 5z * 4) + z(2 + 5z)) = 0 ((8 + 20z) + z(2 + 5z)) = 0 (8 + 20z + (2 * z + 5z * z)) = 0 (8 + 20z + (2z + 5z2)) = 0 Combine like terms: 20z + 2z = 22z (8 + 22z + 5z2) = 0 Solving 8 + 22z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + z)(2 + 5z) = 0Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Subproblem 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 = {-4, -0.4}
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