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Simplifying 3(x + 2) * 6(-3 + -1x) = 4(2x + -1) Reorder the terms: 3(2 + x) * 6(-3 + -1x) = 4(2x + -1) Reorder the terms for easier multiplication: 3 * 6(2 + x)(-3 + -1x) = 4(2x + -1) Multiply 3 * 6 18(2 + x)(-3 + -1x) = 4(2x + -1) Multiply (2 + x) * (-3 + -1x) 18(2(-3 + -1x) + x(-3 + -1x)) = 4(2x + -1) 18((-3 * 2 + -1x * 2) + x(-3 + -1x)) = 4(2x + -1) 18((-6 + -2x) + x(-3 + -1x)) = 4(2x + -1) 18(-6 + -2x + (-3 * x + -1x * x)) = 4(2x + -1) 18(-6 + -2x + (-3x + -1x2)) = 4(2x + -1) Combine like terms: -2x + -3x = -5x 18(-6 + -5x + -1x2) = 4(2x + -1) (-6 * 18 + -5x * 18 + -1x2 * 18) = 4(2x + -1) (-108 + -90x + -18x2) = 4(2x + -1) Reorder the terms: -108 + -90x + -18x2 = 4(-1 + 2x) -108 + -90x + -18x2 = (-1 * 4 + 2x * 4) -108 + -90x + -18x2 = (-4 + 8x) Solving -108 + -90x + -18x2 = -4 + 8x Solving for variable 'x'. Reorder the terms: -108 + 4 + -90x + -8x + -18x2 = -4 + 8x + 4 + -8x Combine like terms: -108 + 4 = -104 -104 + -90x + -8x + -18x2 = -4 + 8x + 4 + -8x Combine like terms: -90x + -8x = -98x -104 + -98x + -18x2 = -4 + 8x + 4 + -8x Reorder the terms: -104 + -98x + -18x2 = -4 + 4 + 8x + -8x Combine like terms: -4 + 4 = 0 -104 + -98x + -18x2 = 0 + 8x + -8x -104 + -98x + -18x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -104 + -98x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(52 + 49x + 9x2) = 0 Factor a trinomial. -2((4 + x)(13 + 9x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(13 + 9x)' equal to zero and attempt to solve: Simplifying 13 + 9x = 0 Solving 13 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 9x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 9x = 0 + -13 9x = 0 + -13 Combine like terms: 0 + -13 = -13 9x = -13 Divide each side by '9'. x = -1.444444444 Simplifying x = -1.444444444Solution
x = {-4, -1.444444444}
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