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Simplifying -6(4b + 2)(25b + -2) = 0 Reorder the terms: -6(2 + 4b)(25b + -2) = 0 Reorder the terms: -6(2 + 4b)(-2 + 25b) = 0 Multiply (2 + 4b) * (-2 + 25b) -6(2(-2 + 25b) + 4b * (-2 + 25b)) = 0 -6((-2 * 2 + 25b * 2) + 4b * (-2 + 25b)) = 0 -6((-4 + 50b) + 4b * (-2 + 25b)) = 0 -6(-4 + 50b + (-2 * 4b + 25b * 4b)) = 0 -6(-4 + 50b + (-8b + 100b2)) = 0 Combine like terms: 50b + -8b = 42b -6(-4 + 42b + 100b2) = 0 (-4 * -6 + 42b * -6 + 100b2 * -6) = 0 (24 + -252b + -600b2) = 0 Solving 24 + -252b + -600b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '12'. 12(2 + -21b + -50b2) = 0 Factor a trinomial. 12((2 + -25b)(1 + 2b)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(2 + -25b)' equal to zero and attempt to solve: Simplifying 2 + -25b = 0 Solving 2 + -25b = 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 + -25b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -25b = 0 + -2 -25b = 0 + -2 Combine like terms: 0 + -2 = -2 -25b = -2 Divide each side by '-25'. b = 0.08 Simplifying b = 0.08Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve: Simplifying 1 + 2b = 0 Solving 1 + 2b = 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 + 2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2b = 0 + -1 2b = 0 + -1 Combine like terms: 0 + -1 = -1 2b = -1 Divide each side by '2'. b = -0.5 Simplifying b = -0.5Solution
b = {0.08, -0.5}
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