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Simplifying 6x2 + 2x = 3x + 2 Reorder the terms: 2x + 6x2 = 3x + 2 Reorder the terms: 2x + 6x2 = 2 + 3x Solving 2x + 6x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: -2 + 2x + -3x + 6x2 = 2 + 3x + -2 + -3x Combine like terms: 2x + -3x = -1x -2 + -1x + 6x2 = 2 + 3x + -2 + -3x Reorder the terms: -2 + -1x + 6x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 -2 + -1x + 6x2 = 0 + 3x + -3x -2 + -1x + 6x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -2 + -1x + 6x2 = 0 Factor a trinomial. (-1 + -2x)(2 + -3x) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.5, 0.6666666667}
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