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Simplifying (3x + -2)(4 + -1x) + -1(2x + -3) = 7 + -3x Reorder the terms: (-2 + 3x)(4 + -1x) + -1(2x + -3) = 7 + -3x Multiply (-2 + 3x) * (4 + -1x) (-2(4 + -1x) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x ((4 * -2 + -1x * -2) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x ((-8 + 2x) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x (-8 + 2x + (4 * 3x + -1x * 3x)) + -1(2x + -3) = 7 + -3x (-8 + 2x + (12x + -3x2)) + -1(2x + -3) = 7 + -3x Combine like terms: 2x + 12x = 14x (-8 + 14x + -3x2) + -1(2x + -3) = 7 + -3x Reorder the terms: -8 + 14x + -3x2 + -1(-3 + 2x) = 7 + -3x -8 + 14x + -3x2 + (-3 * -1 + 2x * -1) = 7 + -3x -8 + 14x + -3x2 + (3 + -2x) = 7 + -3x Reorder the terms: -8 + 3 + 14x + -2x + -3x2 = 7 + -3x Combine like terms: -8 + 3 = -5 -5 + 14x + -2x + -3x2 = 7 + -3x Combine like terms: 14x + -2x = 12x -5 + 12x + -3x2 = 7 + -3x Solving -5 + 12x + -3x2 = 7 + -3x Solving for variable 'x'. Reorder the terms: -5 + -7 + 12x + 3x + -3x2 = 7 + -3x + -7 + 3x Combine like terms: -5 + -7 = -12 -12 + 12x + 3x + -3x2 = 7 + -3x + -7 + 3x Combine like terms: 12x + 3x = 15x -12 + 15x + -3x2 = 7 + -3x + -7 + 3x Reorder the terms: -12 + 15x + -3x2 = 7 + -7 + -3x + 3x Combine like terms: 7 + -7 = 0 -12 + 15x + -3x2 = 0 + -3x + 3x -12 + 15x + -3x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -12 + 15x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5x + -1x2) = 0 Factor a trinomial. 3((-4 + x)(1 + -1x)) = 0 Ignore the factor 3.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {4, 1}
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