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