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Simplifying (5b + -2)(6b + -4) = 0 Reorder the terms: (-2 + 5b)(6b + -4) = 0 Reorder the terms: (-2 + 5b)(-4 + 6b) = 0 Multiply (-2 + 5b) * (-4 + 6b) (-2(-4 + 6b) + 5b * (-4 + 6b)) = 0 ((-4 * -2 + 6b * -2) + 5b * (-4 + 6b)) = 0 ((8 + -12b) + 5b * (-4 + 6b)) = 0 (8 + -12b + (-4 * 5b + 6b * 5b)) = 0 (8 + -12b + (-20b + 30b2)) = 0 Combine like terms: -12b + -20b = -32b (8 + -32b + 30b2) = 0 Solving 8 + -32b + 30b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -16b + 15b2) = 0 Factor a trinomial. 2((2 + -5b)(2 + -3b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5b)' equal to zero and attempt to solve: Simplifying 2 + -5b = 0 Solving 2 + -5b = 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 + -5b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5b = 0 + -2 -5b = 0 + -2 Combine like terms: 0 + -2 = -2 -5b = -2 Divide each side by '-5'. b = 0.4 Simplifying b = 0.4Subproblem 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 = {0.4, 0.6666666667}
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