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Simplifying (18z + -6)(12z + -14) = 0 Reorder the terms: (-6 + 18z)(12z + -14) = 0 Reorder the terms: (-6 + 18z)(-14 + 12z) = 0 Multiply (-6 + 18z) * (-14 + 12z) (-6(-14 + 12z) + 18z * (-14 + 12z)) = 0 ((-14 * -6 + 12z * -6) + 18z * (-14 + 12z)) = 0 ((84 + -72z) + 18z * (-14 + 12z)) = 0 (84 + -72z + (-14 * 18z + 12z * 18z)) = 0 (84 + -72z + (-252z + 216z2)) = 0 Combine like terms: -72z + -252z = -324z (84 + -324z + 216z2) = 0 Solving 84 + -324z + 216z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '12'. 12(7 + -27z + 18z2) = 0 Factor a trinomial. 12((1 + -3z)(7 + -6z)) = 0 Ignore the factor 12.Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(7 + -6z)' equal to zero and attempt to solve: Simplifying 7 + -6z = 0 Solving 7 + -6z = 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 + -6z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6z = 0 + -7 -6z = 0 + -7 Combine like terms: 0 + -7 = -7 -6z = -7 Divide each side by '-6'. z = 1.166666667 Simplifying z = 1.166666667Solution
z = {0.3333333333, 1.166666667}
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