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Simplifying x3 + -5x2 + -2x + 24 = (x + -4)(x2 + -1x + -6) Reorder the terms: 24 + -2x + -5x2 + x3 = (x + -4)(x2 + -1x + -6) Reorder the terms: 24 + -2x + -5x2 + x3 = (-4 + x)(x2 + -1x + -6) Reorder the terms: 24 + -2x + -5x2 + x3 = (-4 + x)(-6 + -1x + x2) Multiply (-4 + x) * (-6 + -1x + x2) 24 + -2x + -5x2 + x3 = (-4(-6 + -1x + x2) + x(-6 + -1x + x2)) 24 + -2x + -5x2 + x3 = ((-6 * -4 + -1x * -4 + x2 * -4) + x(-6 + -1x + x2)) 24 + -2x + -5x2 + x3 = ((24 + 4x + -4x2) + x(-6 + -1x + x2)) 24 + -2x + -5x2 + x3 = (24 + 4x + -4x2 + (-6 * x + -1x * x + x2 * x)) 24 + -2x + -5x2 + x3 = (24 + 4x + -4x2 + (-6x + -1x2 + x3)) Reorder the terms: 24 + -2x + -5x2 + x3 = (24 + 4x + -6x + -4x2 + -1x2 + x3) Combine like terms: 4x + -6x = -2x 24 + -2x + -5x2 + x3 = (24 + -2x + -4x2 + -1x2 + x3) Combine like terms: -4x2 + -1x2 = -5x2 24 + -2x + -5x2 + x3 = (24 + -2x + -5x2 + x3) Add '-24' to each side of the equation. 24 + -2x + -5x2 + -24 + x3 = 24 + -2x + -5x2 + -24 + x3 Reorder the terms: 24 + -24 + -2x + -5x2 + x3 = 24 + -2x + -5x2 + -24 + x3 Combine like terms: 24 + -24 = 0 0 + -2x + -5x2 + x3 = 24 + -2x + -5x2 + -24 + x3 -2x + -5x2 + x3 = 24 + -2x + -5x2 + -24 + x3 Reorder the terms: -2x + -5x2 + x3 = 24 + -24 + -2x + -5x2 + x3 Combine like terms: 24 + -24 = 0 -2x + -5x2 + x3 = 0 + -2x + -5x2 + x3 -2x + -5x2 + x3 = -2x + -5x2 + x3 Add '2x' to each side of the equation. -2x + -5x2 + 2x + x3 = -2x + -5x2 + 2x + x3 Reorder the terms: -2x + 2x + -5x2 + x3 = -2x + -5x2 + 2x + x3 Combine like terms: -2x + 2x = 0 0 + -5x2 + x3 = -2x + -5x2 + 2x + x3 -5x2 + x3 = -2x + -5x2 + 2x + x3 Reorder the terms: -5x2 + x3 = -2x + 2x + -5x2 + x3 Combine like terms: -2x + 2x = 0 -5x2 + x3 = 0 + -5x2 + x3 -5x2 + x3 = -5x2 + x3 Add '5x2' to each side of the equation. -5x2 + 5x2 + x3 = -5x2 + 5x2 + x3 Combine like terms: -5x2 + 5x2 = 0 0 + x3 = -5x2 + 5x2 + x3 x3 = -5x2 + 5x2 + x3 Combine like terms: -5x2 + 5x2 = 0 x3 = 0 + x3 x3 = x3 Add '-1x3' to each side of the equation. x3 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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