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Simplifying 27b(b + 3) = 3510 Reorder the terms: 27b(3 + b) = 3510 (3 * 27b + b * 27b) = 3510 (81b + 27b2) = 3510 Solving 81b + 27b2 = 3510 Solving for variable 'b'. Reorder the terms: -3510 + 81b + 27b2 = 3510 + -3510 Combine like terms: 3510 + -3510 = 0 -3510 + 81b + 27b2 = 0 Factor out the Greatest Common Factor (GCF), '27'. 27(-130 + 3b + b2) = 0 Factor a trinomial. 27((-13 + -1b)(10 + -1b)) = 0 Ignore the factor 27.Subproblem 1
Set the factor '(-13 + -1b)' equal to zero and attempt to solve: Simplifying -13 + -1b = 0 Solving -13 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1b = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1b = 0 + 13 -1b = 0 + 13 Combine like terms: 0 + 13 = 13 -1b = 13 Divide each side by '-1'. b = -13 Simplifying b = -13Subproblem 2
Set the factor '(10 + -1b)' equal to zero and attempt to solve: Simplifying 10 + -1b = 0 Solving 10 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1b = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1b = 0 + -10 -1b = 0 + -10 Combine like terms: 0 + -10 = -10 -1b = -10 Divide each side by '-1'. b = 10 Simplifying b = 10Solution
b = {-13, 10}
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