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Simplifying z(3z + -1) + 2(4z + 5) = 8 Reorder the terms: z(-1 + 3z) + 2(4z + 5) = 8 (-1 * z + 3z * z) + 2(4z + 5) = 8 (-1z + 3z2) + 2(4z + 5) = 8 Reorder the terms: -1z + 3z2 + 2(5 + 4z) = 8 -1z + 3z2 + (5 * 2 + 4z * 2) = 8 -1z + 3z2 + (10 + 8z) = 8 Reorder the terms: 10 + -1z + 8z + 3z2 = 8 Combine like terms: -1z + 8z = 7z 10 + 7z + 3z2 = 8 Solving 10 + 7z + 3z2 = 8 Solving for variable 'z'. Reorder the terms: 10 + -8 + 7z + 3z2 = 8 + -8 Combine like terms: 10 + -8 = 2 2 + 7z + 3z2 = 8 + -8 Combine like terms: 8 + -8 = 0 2 + 7z + 3z2 = 0 Factor a trinomial. (2 + z)(1 + 3z) = 0Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {-2, -0.3333333333}
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