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Simplifying 14b = 16b(b + 12) Reorder the terms: 14b = 16b(12 + b) 14b = (12 * 16b + b * 16b) 14b = (192b + 16b2) Solving 14b = 192b + 16b2 Solving for variable 'b'. Combine like terms: 14b + -192b = -178b -178b + -16b2 = 192b + 16b2 + -192b + -16b2 Reorder the terms: -178b + -16b2 = 192b + -192b + 16b2 + -16b2 Combine like terms: 192b + -192b = 0 -178b + -16b2 = 0 + 16b2 + -16b2 -178b + -16b2 = 16b2 + -16b2 Combine like terms: 16b2 + -16b2 = 0 -178b + -16b2 = 0 Factor out the Greatest Common Factor (GCF), '-2b'. -2b(89 + 8b) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(89 + 8b)' equal to zero and attempt to solve: Simplifying 89 + 8b = 0 Solving 89 + 8b = 0 Move all terms containing b to the left, all other terms to the right. Add '-89' to each side of the equation. 89 + -89 + 8b = 0 + -89 Combine like terms: 89 + -89 = 0 0 + 8b = 0 + -89 8b = 0 + -89 Combine like terms: 0 + -89 = -89 8b = -89 Divide each side by '8'. b = -11.125 Simplifying b = -11.125Solution
b = {0, -11.125}
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