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Simplifying (2 + -1z)(3z + 8) = 0 Reorder the terms: (2 + -1z)(8 + 3z) = 0 Multiply (2 + -1z) * (8 + 3z) (2(8 + 3z) + -1z * (8 + 3z)) = 0 ((8 * 2 + 3z * 2) + -1z * (8 + 3z)) = 0 ((16 + 6z) + -1z * (8 + 3z)) = 0 (16 + 6z + (8 * -1z + 3z * -1z)) = 0 (16 + 6z + (-8z + -3z2)) = 0 Combine like terms: 6z + -8z = -2z (16 + -2z + -3z2) = 0 Solving 16 + -2z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(8 + 3z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve: Simplifying 8 + 3z = 0 Solving 8 + 3z = 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 + 3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3z = 0 + -8 3z = 0 + -8 Combine like terms: 0 + -8 = -8 3z = -8 Divide each side by '3'. z = -2.666666667 Simplifying z = -2.666666667Solution
z = {2, -2.666666667}
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