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Simplifying (4x + -1)(2x + 3) = (x + 3)(x + -1) Reorder the terms: (-1 + 4x)(2x + 3) = (x + 3)(x + -1) Reorder the terms: (-1 + 4x)(3 + 2x) = (x + 3)(x + -1) Multiply (-1 + 4x) * (3 + 2x) (-1(3 + 2x) + 4x * (3 + 2x)) = (x + 3)(x + -1) ((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = (x + 3)(x + -1) ((-3 + -2x) + 4x * (3 + 2x)) = (x + 3)(x + -1) (-3 + -2x + (3 * 4x + 2x * 4x)) = (x + 3)(x + -1) (-3 + -2x + (12x + 8x2)) = (x + 3)(x + -1) Combine like terms: -2x + 12x = 10x (-3 + 10x + 8x2) = (x + 3)(x + -1) Reorder the terms: -3 + 10x + 8x2 = (3 + x)(x + -1) Reorder the terms: -3 + 10x + 8x2 = (3 + x)(-1 + x) Multiply (3 + x) * (-1 + x) -3 + 10x + 8x2 = (3(-1 + x) + x(-1 + x)) -3 + 10x + 8x2 = ((-1 * 3 + x * 3) + x(-1 + x)) -3 + 10x + 8x2 = ((-3 + 3x) + x(-1 + x)) -3 + 10x + 8x2 = (-3 + 3x + (-1 * x + x * x)) -3 + 10x + 8x2 = (-3 + 3x + (-1x + x2)) Combine like terms: 3x + -1x = 2x -3 + 10x + 8x2 = (-3 + 2x + x2) Add '3' to each side of the equation. -3 + 10x + 3 + 8x2 = -3 + 2x + 3 + x2 Reorder the terms: -3 + 3 + 10x + 8x2 = -3 + 2x + 3 + x2 Combine like terms: -3 + 3 = 0 0 + 10x + 8x2 = -3 + 2x + 3 + x2 10x + 8x2 = -3 + 2x + 3 + x2 Reorder the terms: 10x + 8x2 = -3 + 3 + 2x + x2 Combine like terms: -3 + 3 = 0 10x + 8x2 = 0 + 2x + x2 10x + 8x2 = 2x + x2 Solving 10x + 8x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: 10x + -2x + 8x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 10x + -2x = 8x 8x + 8x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 8x2 + -1x2 = 7x2 8x + 7x2 = 2x + x2 + -2x + -1x2 Reorder the terms: 8x + 7x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 8x + 7x2 = 0 + x2 + -1x2 8x + 7x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(8 + 7x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + 7x)' equal to zero and attempt to solve: Simplifying 8 + 7x = 0 Solving 8 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7x = 0 + -8 7x = 0 + -8 Combine like terms: 0 + -8 = -8 7x = -8 Divide each side by '7'. x = -1.142857143 Simplifying x = -1.142857143Solution
x = {0, -1.142857143}
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