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Simplifying -1x2 + -10x + -21 = 2x2 + 20x + 51 Reorder the terms: -21 + -10x + -1x2 = 2x2 + 20x + 51 Reorder the terms: -21 + -10x + -1x2 = 51 + 20x + 2x2 Solving -21 + -10x + -1x2 = 51 + 20x + 2x2 Solving for variable 'x'. Reorder the terms: -21 + -51 + -10x + -20x + -1x2 + -2x2 = 51 + 20x + 2x2 + -51 + -20x + -2x2 Combine like terms: -21 + -51 = -72 -72 + -10x + -20x + -1x2 + -2x2 = 51 + 20x + 2x2 + -51 + -20x + -2x2 Combine like terms: -10x + -20x = -30x -72 + -30x + -1x2 + -2x2 = 51 + 20x + 2x2 + -51 + -20x + -2x2 Combine like terms: -1x2 + -2x2 = -3x2 -72 + -30x + -3x2 = 51 + 20x + 2x2 + -51 + -20x + -2x2 Reorder the terms: -72 + -30x + -3x2 = 51 + -51 + 20x + -20x + 2x2 + -2x2 Combine like terms: 51 + -51 = 0 -72 + -30x + -3x2 = 0 + 20x + -20x + 2x2 + -2x2 -72 + -30x + -3x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 -72 + -30x + -3x2 = 0 + 2x2 + -2x2 -72 + -30x + -3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -72 + -30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(24 + 10x + x2) = 0 Factor a trinomial. -3((6 + x)(4 + x)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-6, -4}
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