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Simplifying (8z + -7)(z + -3) = 0 Reorder the terms: (-7 + 8z)(z + -3) = 0 Reorder the terms: (-7 + 8z)(-3 + z) = 0 Multiply (-7 + 8z) * (-3 + z) (-7(-3 + z) + 8z * (-3 + z)) = 0 ((-3 * -7 + z * -7) + 8z * (-3 + z)) = 0 ((21 + -7z) + 8z * (-3 + z)) = 0 (21 + -7z + (-3 * 8z + z * 8z)) = 0 (21 + -7z + (-24z + 8z2)) = 0 Combine like terms: -7z + -24z = -31z (21 + -31z + 8z2) = 0 Solving 21 + -31z + 8z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -8z)(3 + -1z) = 0Subproblem 1
Set the factor '(7 + -8z)' equal to zero and attempt to solve: Simplifying 7 + -8z = 0 Solving 7 + -8z = 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 + -8z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8z = 0 + -7 -8z = 0 + -7 Combine like terms: 0 + -7 = -7 -8z = -7 Divide each side by '-8'. z = 0.875 Simplifying z = 0.875Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {0.875, 3}
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