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Simplifying 3x2 + 5x + 4 = 2x2 + 4x + 6 Reorder the terms: 4 + 5x + 3x2 = 2x2 + 4x + 6 Reorder the terms: 4 + 5x + 3x2 = 6 + 4x + 2x2 Solving 4 + 5x + 3x2 = 6 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + -6 + 5x + -4x + 3x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: 4 + -6 = -2 -2 + 5x + -4x + 3x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: 5x + -4x = 1x -2 + 1x + 3x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -2 + 1x + 1x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Reorder the terms: -2 + 1x + 1x2 = 6 + -6 + 4x + -4x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -2 + 1x + 1x2 = 0 + 4x + -4x + 2x2 + -2x2 -2 + 1x + 1x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -2 + 1x + 1x2 = 0 + 2x2 + -2x2 -2 + 1x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2 + 1x + 1x2 = 0 Factor a trinomial. (-2 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 1Solution
x = {-2, 1}
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