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Simplifying (7 + z)(5z + 2) = 0 Reorder the terms: (7 + z)(2 + 5z) = 0 Multiply (7 + z) * (2 + 5z) (7(2 + 5z) + z(2 + 5z)) = 0 ((2 * 7 + 5z * 7) + z(2 + 5z)) = 0 ((14 + 35z) + z(2 + 5z)) = 0 (14 + 35z + (2 * z + 5z * z)) = 0 (14 + 35z + (2z + 5z2)) = 0 Combine like terms: 35z + 2z = 37z (14 + 37z + 5z2) = 0 Solving 14 + 37z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + z)(2 + 5z) = 0Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 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 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 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 = {-7, -0.4}
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