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Simplifying (2x + -3)(3x + -4) + -1(x + -13x)(x + -4) = 40 Reorder the terms: (-3 + 2x)(3x + -4) + -1(x + -13x)(x + -4) = 40 Reorder the terms: (-3 + 2x)(-4 + 3x) + -1(x + -13x)(x + -4) = 40 Multiply (-3 + 2x) * (-4 + 3x) (-3(-4 + 3x) + 2x * (-4 + 3x)) + -1(x + -13x)(x + -4) = 40 ((-4 * -3 + 3x * -3) + 2x * (-4 + 3x)) + -1(x + -13x)(x + -4) = 40 ((12 + -9x) + 2x * (-4 + 3x)) + -1(x + -13x)(x + -4) = 40 (12 + -9x + (-4 * 2x + 3x * 2x)) + -1(x + -13x)(x + -4) = 40 (12 + -9x + (-8x + 6x2)) + -1(x + -13x)(x + -4) = 40 Combine like terms: -9x + -8x = -17x (12 + -17x + 6x2) + -1(x + -13x)(x + -4) = 40 Combine like terms: x + -13x = -12x 12 + -17x + 6x2 + -1(-12x)(x + -4) = 40 Remove parenthesis around (-12x) 12 + -17x + 6x2 + -1 * -12x(x + -4) = 40 Reorder the terms: 12 + -17x + 6x2 + -1 * -12x(-4 + x) = 40 Multiply -1 * -12 12 + -17x + 6x2 + 12x(-4 + x) = 40 12 + -17x + 6x2 + (-4 * 12x + x * 12x) = 40 12 + -17x + 6x2 + (-48x + 12x2) = 40 Reorder the terms: 12 + -17x + -48x + 6x2 + 12x2 = 40 Combine like terms: -17x + -48x = -65x 12 + -65x + 6x2 + 12x2 = 40 Combine like terms: 6x2 + 12x2 = 18x2 12 + -65x + 18x2 = 40 Solving 12 + -65x + 18x2 = 40 Solving for variable 'x'. Reorder the terms: 12 + -40 + -65x + 18x2 = 40 + -40 Combine like terms: 12 + -40 = -28 -28 + -65x + 18x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -28 + -65x + 18x2 = 0 Factor a trinomial. (-7 + -18x)(4 + -1x) = 0Subproblem 1
Set the factor '(-7 + -18x)' equal to zero and attempt to solve: Simplifying -7 + -18x = 0 Solving -7 + -18x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -18x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -18x = 0 + 7 -18x = 0 + 7 Combine like terms: 0 + 7 = 7 -18x = 7 Divide each side by '-18'. x = -0.3888888889 Simplifying x = -0.3888888889Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.3888888889, 4}
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