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Simplifying 14z2 + 21 = 5z2 + 5 + -24z Reorder the terms: 21 + 14z2 = 5z2 + 5 + -24z Reorder the terms: 21 + 14z2 = 5 + -24z + 5z2 Solving 21 + 14z2 = 5 + -24z + 5z2 Solving for variable 'z'. Reorder the terms: 21 + -5 + 24z + 14z2 + -5z2 = 5 + -24z + 5z2 + -5 + 24z + -5z2 Combine like terms: 21 + -5 = 16 16 + 24z + 14z2 + -5z2 = 5 + -24z + 5z2 + -5 + 24z + -5z2 Combine like terms: 14z2 + -5z2 = 9z2 16 + 24z + 9z2 = 5 + -24z + 5z2 + -5 + 24z + -5z2 Reorder the terms: 16 + 24z + 9z2 = 5 + -5 + -24z + 24z + 5z2 + -5z2 Combine like terms: 5 + -5 = 0 16 + 24z + 9z2 = 0 + -24z + 24z + 5z2 + -5z2 16 + 24z + 9z2 = -24z + 24z + 5z2 + -5z2 Combine like terms: -24z + 24z = 0 16 + 24z + 9z2 = 0 + 5z2 + -5z2 16 + 24z + 9z2 = 5z2 + -5z2 Combine like terms: 5z2 + -5z2 = 0 16 + 24z + 9z2 = 0 Factor a trinomial. (4 + 3z)(4 + 3z) = 0Subproblem 1
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 = -1.333333333Subproblem 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 = {-1.333333333, -1.333333333}
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