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Simplifying 3x2 + 13 = 4x2 + 12x Reorder the terms: 13 + 3x2 = 4x2 + 12x Reorder the terms: 13 + 3x2 = 12x + 4x2 Solving 13 + 3x2 = 12x + 4x2 Solving for variable 'x'. Reorder the terms: 13 + -12x + 3x2 + -4x2 = 12x + 4x2 + -12x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 13 + -12x + -1x2 = 12x + 4x2 + -12x + -4x2 Reorder the terms: 13 + -12x + -1x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 13 + -12x + -1x2 = 0 + 4x2 + -4x2 13 + -12x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 13 + -12x + -1x2 = 0 Factor a trinomial. (1 + -1x)(13 + x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Simplifying x = -13Solution
x = {1, -13}
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