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Simplifying x2 + 23x + 76 = 4x2 + 8x + 4 Reorder the terms: 76 + 23x + x2 = 4x2 + 8x + 4 Reorder the terms: 76 + 23x + x2 = 4 + 8x + 4x2 Solving 76 + 23x + x2 = 4 + 8x + 4x2 Solving for variable 'x'. Reorder the terms: 76 + -4 + 23x + -8x + x2 + -4x2 = 4 + 8x + 4x2 + -4 + -8x + -4x2 Combine like terms: 76 + -4 = 72 72 + 23x + -8x + x2 + -4x2 = 4 + 8x + 4x2 + -4 + -8x + -4x2 Combine like terms: 23x + -8x = 15x 72 + 15x + x2 + -4x2 = 4 + 8x + 4x2 + -4 + -8x + -4x2 Combine like terms: x2 + -4x2 = -3x2 72 + 15x + -3x2 = 4 + 8x + 4x2 + -4 + -8x + -4x2 Reorder the terms: 72 + 15x + -3x2 = 4 + -4 + 8x + -8x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 72 + 15x + -3x2 = 0 + 8x + -8x + 4x2 + -4x2 72 + 15x + -3x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 72 + 15x + -3x2 = 0 + 4x2 + -4x2 72 + 15x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 72 + 15x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(24 + 5x + -1x2) = 0 Factor a trinomial. 3((8 + -1x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {8, -3}
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