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Simplifying 2((-13 + -2b)(4 + -1b)) = 0 Multiply (-13 + -2b) * (4 + -1b) 2((-13(4 + -1b) + -2b * (4 + -1b))) = 0 2(((4 * -13 + -1b * -13) + -2b * (4 + -1b))) = 0 2(((-52 + 13b) + -2b * (4 + -1b))) = 0 2((-52 + 13b + (4 * -2b + -1b * -2b))) = 0 2((-52 + 13b + (-8b + 2b2))) = 0 Combine like terms: 13b + -8b = 5b 2((-52 + 5b + 2b2)) = 0 (-52 * 2 + 5b * 2 + 2b2 * 2) = 0 (-104 + 10b + 4b2) = 0 Solving -104 + 10b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + 5b + 2b2) = 0 Factor a trinomial. 2((-13 + -2b)(4 + -1b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -2b)' equal to zero and attempt to solve: Simplifying -13 + -2b = 0 Solving -13 + -2b = 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 + -2b = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2b = 0 + 13 -2b = 0 + 13 Combine like terms: 0 + 13 = 13 -2b = 13 Divide each side by '-2'. b = -6.5 Simplifying b = -6.5Subproblem 2
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 = 4Solution
b = {-6.5, 4}
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