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Simplifying 6x2 + -4x + 6 = 4x2 + 3x + 3 Reorder the terms: 6 + -4x + 6x2 = 4x2 + 3x + 3 Reorder the terms: 6 + -4x + 6x2 = 3 + 3x + 4x2 Solving 6 + -4x + 6x2 = 3 + 3x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -3 + -4x + -3x + 6x2 + -4x2 = 3 + 3x + 4x2 + -3 + -3x + -4x2 Combine like terms: 6 + -3 = 3 3 + -4x + -3x + 6x2 + -4x2 = 3 + 3x + 4x2 + -3 + -3x + -4x2 Combine like terms: -4x + -3x = -7x 3 + -7x + 6x2 + -4x2 = 3 + 3x + 4x2 + -3 + -3x + -4x2 Combine like terms: 6x2 + -4x2 = 2x2 3 + -7x + 2x2 = 3 + 3x + 4x2 + -3 + -3x + -4x2 Reorder the terms: 3 + -7x + 2x2 = 3 + -3 + 3x + -3x + 4x2 + -4x2 Combine like terms: 3 + -3 = 0 3 + -7x + 2x2 = 0 + 3x + -3x + 4x2 + -4x2 3 + -7x + 2x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 3 + -7x + 2x2 = 0 + 4x2 + -4x2 3 + -7x + 2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + -7x + 2x2 = 0 Factor a trinomial. (1 + -2x)(3 + -1x) = 0Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0.5, 3}
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