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Simplifying (6b + 10)(6b + -4) = 0 Reorder the terms: (10 + 6b)(6b + -4) = 0 Reorder the terms: (10 + 6b)(-4 + 6b) = 0 Multiply (10 + 6b) * (-4 + 6b) (10(-4 + 6b) + 6b * (-4 + 6b)) = 0 ((-4 * 10 + 6b * 10) + 6b * (-4 + 6b)) = 0 ((-40 + 60b) + 6b * (-4 + 6b)) = 0 (-40 + 60b + (-4 * 6b + 6b * 6b)) = 0 (-40 + 60b + (-24b + 36b2)) = 0 Combine like terms: 60b + -24b = 36b (-40 + 36b + 36b2) = 0 Solving -40 + 36b + 36b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 9b + 9b2) = 0 Factor a trinomial. 4((-5 + -3b)(2 + -3b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve: Simplifying -5 + -3b = 0 Solving -5 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3b = 0 + 5 -3b = 0 + 5 Combine like terms: 0 + 5 = 5 -3b = 5 Divide each side by '-3'. b = -1.666666667 Simplifying b = -1.666666667Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667Solution
b = {-1.666666667, 0.6666666667}
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