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Simplifying (7 + -1z)(3z + 8) = 0 Reorder the terms: (7 + -1z)(8 + 3z) = 0 Multiply (7 + -1z) * (8 + 3z) (7(8 + 3z) + -1z * (8 + 3z)) = 0 ((8 * 7 + 3z * 7) + -1z * (8 + 3z)) = 0 ((56 + 21z) + -1z * (8 + 3z)) = 0 (56 + 21z + (8 * -1z + 3z * -1z)) = 0 (56 + 21z + (-8z + -3z2)) = 0 Combine like terms: 21z + -8z = 13z (56 + 13z + -3z2) = 0 Solving 56 + 13z + -3z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(8 + 3z) = 0Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Subproblem 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 = {7, -2.666666667}
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