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Simplifying 6b2 = 48 + -42b Solving 6b2 = 48 + -42b Solving for variable 'b'. Reorder the terms: -48 + 42b + 6b2 = 48 + -42b + -48 + 42b Reorder the terms: -48 + 42b + 6b2 = 48 + -48 + -42b + 42b Combine like terms: 48 + -48 = 0 -48 + 42b + 6b2 = 0 + -42b + 42b -48 + 42b + 6b2 = -42b + 42b Combine like terms: -42b + 42b = 0 -48 + 42b + 6b2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 7b + b2) = 0 Factor a trinomial. 6((-8 + -1b)(1 + -1b)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve: Simplifying -8 + -1b = 0 Solving -8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1b = 0 + 8 -1b = 0 + 8 Combine like terms: 0 + 8 = 8 -1b = 8 Divide each side by '-1'. b = -8 Simplifying b = -8Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {-8, 1}
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