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Simplifying x + 6 = 4x2 + -12x + 9 Reorder the terms: 6 + x = 4x2 + -12x + 9 Reorder the terms: 6 + x = 9 + -12x + 4x2 Solving 6 + x = 9 + -12x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -9 + x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Combine like terms: 6 + -9 = -3 -3 + x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Combine like terms: x + 12x = 13x -3 + 13x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Reorder the terms: -3 + 13x + -4x2 = 9 + -9 + -12x + 12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -3 + 13x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2 -3 + 13x + -4x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 -3 + 13x + -4x2 = 0 + 4x2 + -4x2 -3 + 13x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 13x + -4x2 = 0 Factor a trinomial. (-3 + x)(1 + -4x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {3, 0.25}
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