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Simplifying 2z(3z + 14) = 48 Reorder the terms: 2z(14 + 3z) = 48 (14 * 2z + 3z * 2z) = 48 (28z + 6z2) = 48 Solving 28z + 6z2 = 48 Solving for variable 'z'. Reorder the terms: -48 + 28z + 6z2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 28z + 6z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 14z + 3z2) = 0 Factor a trinomial. 2((-6 + -1z)(4 + -3z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 2
Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 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 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {-6, 1.333333333}
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