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Simplifying -10 + 6b = 8 + -4b2 Solving -10 + 6b = 8 + -4b2 Solving for variable 'b'. Reorder the terms: -10 + -8 + 6b + 4b2 = 8 + -4b2 + -8 + 4b2 Combine like terms: -10 + -8 = -18 -18 + 6b + 4b2 = 8 + -4b2 + -8 + 4b2 Reorder the terms: -18 + 6b + 4b2 = 8 + -8 + -4b2 + 4b2 Combine like terms: 8 + -8 = 0 -18 + 6b + 4b2 = 0 + -4b2 + 4b2 -18 + 6b + 4b2 = -4b2 + 4b2 Combine like terms: -4b2 + 4b2 = 0 -18 + 6b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 3b + 2b2) = 0 Factor a trinomial. 2((-3 + -1b)(3 + -2b)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Solution
b = {-3, 1.5}
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