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Simplifying 3z(3z + 10) = 24 Reorder the terms: 3z(10 + 3z) = 24 (10 * 3z + 3z * 3z) = 24 (30z + 9z2) = 24 Solving 30z + 9z2 = 24 Solving for variable 'z'. Reorder the terms: -24 + 30z + 9z2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 30z + 9z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 10z + 3z2) = 0 Factor a trinomial. 3((-4 + -1z)(2 + -3z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 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 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {-4, 0.6666666667}
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