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Simplifying 4x2 + -84 = 5x2 + 19x Reorder the terms: -84 + 4x2 = 5x2 + 19x Reorder the terms: -84 + 4x2 = 19x + 5x2 Solving -84 + 4x2 = 19x + 5x2 Solving for variable 'x'. Reorder the terms: -84 + -19x + 4x2 + -5x2 = 19x + 5x2 + -19x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -84 + -19x + -1x2 = 19x + 5x2 + -19x + -5x2 Reorder the terms: -84 + -19x + -1x2 = 19x + -19x + 5x2 + -5x2 Combine like terms: 19x + -19x = 0 -84 + -19x + -1x2 = 0 + 5x2 + -5x2 -84 + -19x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -84 + -19x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(84 + 19x + x2) = 0 Factor a trinomial. -1((12 + x)(7 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {-12, -7}
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