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Simplifying 3x2 + 5x + 2 = -3x2 + x + 4 Reorder the terms: 2 + 5x + 3x2 = -3x2 + x + 4 Reorder the terms: 2 + 5x + 3x2 = 4 + x + -3x2 Solving 2 + 5x + 3x2 = 4 + x + -3x2 Solving for variable 'x'. Reorder the terms: 2 + -4 + 5x + -1x + 3x2 + 3x2 = 4 + x + -3x2 + -4 + -1x + 3x2 Combine like terms: 2 + -4 = -2 -2 + 5x + -1x + 3x2 + 3x2 = 4 + x + -3x2 + -4 + -1x + 3x2 Combine like terms: 5x + -1x = 4x -2 + 4x + 3x2 + 3x2 = 4 + x + -3x2 + -4 + -1x + 3x2 Combine like terms: 3x2 + 3x2 = 6x2 -2 + 4x + 6x2 = 4 + x + -3x2 + -4 + -1x + 3x2 Reorder the terms: -2 + 4x + 6x2 = 4 + -4 + x + -1x + -3x2 + 3x2 Combine like terms: 4 + -4 = 0 -2 + 4x + 6x2 = 0 + x + -1x + -3x2 + 3x2 -2 + 4x + 6x2 = x + -1x + -3x2 + 3x2 Combine like terms: x + -1x = 0 -2 + 4x + 6x2 = 0 + -3x2 + 3x2 -2 + 4x + 6x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -2 + 4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + 3x2) = 0 Factor a trinomial. 2((-1 + -1x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-1, 0.3333333333}
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