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Simplifying 3b2 + b = 12 + 2b2 Reorder the terms: b + 3b2 = 12 + 2b2 Solving b + 3b2 = 12 + 2b2 Solving for variable 'b'. Reorder the terms: -12 + b + 3b2 + -2b2 = 12 + 2b2 + -12 + -2b2 Combine like terms: 3b2 + -2b2 = 1b2 -12 + b + 1b2 = 12 + 2b2 + -12 + -2b2 Reorder the terms: -12 + b + 1b2 = 12 + -12 + 2b2 + -2b2 Combine like terms: 12 + -12 = 0 -12 + b + 1b2 = 0 + 2b2 + -2b2 -12 + b + 1b2 = 2b2 + -2b2 Combine like terms: 2b2 + -2b2 = 0 -12 + b + 1b2 = 0 Factor a trinomial. (-4 + -1b)(3 + -1b) = 0Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve: Simplifying -4 + -1b = 0 Solving -4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1b = 0 + 4 -1b = 0 + 4 Combine like terms: 0 + 4 = 4 -1b = 4 Divide each side by '-1'. b = -4 Simplifying b = -4Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-4, 3}
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