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Simplifying (-11b + -6)(-3b + 7) + (-10b + 12)(-11b + -6) = 0 Reorder the terms: (-6 + -11b)(-3b + 7) + (-10b + 12)(-11b + -6) = 0 Reorder the terms: (-6 + -11b)(7 + -3b) + (-10b + 12)(-11b + -6) = 0 Multiply (-6 + -11b) * (7 + -3b) (-6(7 + -3b) + -11b * (7 + -3b)) + (-10b + 12)(-11b + -6) = 0 ((7 * -6 + -3b * -6) + -11b * (7 + -3b)) + (-10b + 12)(-11b + -6) = 0 ((-42 + 18b) + -11b * (7 + -3b)) + (-10b + 12)(-11b + -6) = 0 (-42 + 18b + (7 * -11b + -3b * -11b)) + (-10b + 12)(-11b + -6) = 0 (-42 + 18b + (-77b + 33b2)) + (-10b + 12)(-11b + -6) = 0 Combine like terms: 18b + -77b = -59b (-42 + -59b + 33b2) + (-10b + 12)(-11b + -6) = 0 Reorder the terms: -42 + -59b + 33b2 + (12 + -10b)(-11b + -6) = 0 Reorder the terms: -42 + -59b + 33b2 + (12 + -10b)(-6 + -11b) = 0 Multiply (12 + -10b) * (-6 + -11b) -42 + -59b + 33b2 + (12(-6 + -11b) + -10b * (-6 + -11b)) = 0 -42 + -59b + 33b2 + ((-6 * 12 + -11b * 12) + -10b * (-6 + -11b)) = 0 -42 + -59b + 33b2 + ((-72 + -132b) + -10b * (-6 + -11b)) = 0 -42 + -59b + 33b2 + (-72 + -132b + (-6 * -10b + -11b * -10b)) = 0 -42 + -59b + 33b2 + (-72 + -132b + (60b + 110b2)) = 0 Combine like terms: -132b + 60b = -72b -42 + -59b + 33b2 + (-72 + -72b + 110b2) = 0 Reorder the terms: -42 + -72 + -59b + -72b + 33b2 + 110b2 = 0 Combine like terms: -42 + -72 = -114 -114 + -59b + -72b + 33b2 + 110b2 = 0 Combine like terms: -59b + -72b = -131b -114 + -131b + 33b2 + 110b2 = 0 Combine like terms: 33b2 + 110b2 = 143b2 -114 + -131b + 143b2 = 0 Solving -114 + -131b + 143b2 = 0 Solving for variable 'b'. Factor a trinomial. (-6 + -11b)(19 + -13b) = 0Subproblem 1
Set the factor '(-6 + -11b)' equal to zero and attempt to solve: Simplifying -6 + -11b = 0 Solving -6 + -11b = 0 Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -11b = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -11b = 0 + 6 -11b = 0 + 6 Combine like terms: 0 + 6 = 6 -11b = 6 Divide each side by '-11'. b = -0.5454545455 Simplifying b = -0.5454545455Subproblem 2
Set the factor '(19 + -13b)' equal to zero and attempt to solve: Simplifying 19 + -13b = 0 Solving 19 + -13b = 0 Move all terms containing b to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -13b = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -13b = 0 + -19 -13b = 0 + -19 Combine like terms: 0 + -19 = -19 -13b = -19 Divide each side by '-13'. b = 1.461538462 Simplifying b = 1.461538462Solution
b = {-0.5454545455, 1.461538462}
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