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Simplifying x2 + -7x + -30 = (x + 3)(x + -10) Reorder the terms: -30 + -7x + x2 = (x + 3)(x + -10) Reorder the terms: -30 + -7x + x2 = (3 + x)(x + -10) Reorder the terms: -30 + -7x + x2 = (3 + x)(-10 + x) Multiply (3 + x) * (-10 + x) -30 + -7x + x2 = (3(-10 + x) + x(-10 + x)) -30 + -7x + x2 = ((-10 * 3 + x * 3) + x(-10 + x)) -30 + -7x + x2 = ((-30 + 3x) + x(-10 + x)) -30 + -7x + x2 = (-30 + 3x + (-10 * x + x * x)) -30 + -7x + x2 = (-30 + 3x + (-10x + x2)) Combine like terms: 3x + -10x = -7x -30 + -7x + x2 = (-30 + -7x + x2) Add '30' to each side of the equation. -30 + -7x + 30 + x2 = -30 + -7x + 30 + x2 Reorder the terms: -30 + 30 + -7x + x2 = -30 + -7x + 30 + x2 Combine like terms: -30 + 30 = 0 0 + -7x + x2 = -30 + -7x + 30 + x2 -7x + x2 = -30 + -7x + 30 + x2 Reorder the terms: -7x + x2 = -30 + 30 + -7x + x2 Combine like terms: -30 + 30 = 0 -7x + x2 = 0 + -7x + x2 -7x + x2 = -7x + x2 Add '7x' to each side of the equation. -7x + 7x + x2 = -7x + 7x + x2 Combine like terms: -7x + 7x = 0 0 + x2 = -7x + 7x + x2 x2 = -7x + 7x + x2 Combine like terms: -7x + 7x = 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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