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Simplifying x2 + -2x + -3 = (x + 1)(x + -3) Reorder the terms: -3 + -2x + x2 = (x + 1)(x + -3) Reorder the terms: -3 + -2x + x2 = (1 + x)(x + -3) Reorder the terms: -3 + -2x + x2 = (1 + x)(-3 + x) Multiply (1 + x) * (-3 + x) -3 + -2x + x2 = (1(-3 + x) + x(-3 + x)) -3 + -2x + x2 = ((-3 * 1 + x * 1) + x(-3 + x)) -3 + -2x + x2 = ((-3 + 1x) + x(-3 + x)) -3 + -2x + x2 = (-3 + 1x + (-3 * x + x * x)) -3 + -2x + x2 = (-3 + 1x + (-3x + x2)) Combine like terms: 1x + -3x = -2x -3 + -2x + x2 = (-3 + -2x + x2) Add '3' to each side of the equation. -3 + -2x + 3 + x2 = -3 + -2x + 3 + x2 Reorder the terms: -3 + 3 + -2x + x2 = -3 + -2x + 3 + x2 Combine like terms: -3 + 3 = 0 0 + -2x + x2 = -3 + -2x + 3 + x2 -2x + x2 = -3 + -2x + 3 + x2 Reorder the terms: -2x + x2 = -3 + 3 + -2x + x2 Combine like terms: -3 + 3 = 0 -2x + x2 = 0 + -2x + x2 -2x + x2 = -2x + x2 Add '2x' to each side of the equation. -2x + 2x + x2 = -2x + 2x + x2 Combine like terms: -2x + 2x = 0 0 + x2 = -2x + 2x + x2 x2 = -2x + 2x + x2 Combine like terms: -2x + 2x = 0 x2 = 0 + x2 x2 = x2 Add '-1x2' to each side of the equation. x2 + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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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