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Simplifying 2x(1 + -3x) + -1 + 3x = 0 (1 * 2x + -3x * 2x) + -1 + 3x = 0 (2x + -6x2) + -1 + 3x = 0 Reorder the terms: -1 + 2x + 3x + -6x2 = 0 Combine like terms: 2x + 3x = 5x -1 + 5x + -6x2 = 0 Solving -1 + 5x + -6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + 2x)(1 + -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 '(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 = {0.5, 0.3333333333}
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