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Simplifying 2x(3x + -4) + -1(1 + -3x)(1 + x) = -2 Reorder the terms: 2x(-4 + 3x) + -1(1 + -3x)(1 + x) = -2 (-4 * 2x + 3x * 2x) + -1(1 + -3x)(1 + x) = -2 (-8x + 6x2) + -1(1 + -3x)(1 + x) = -2 Multiply (1 + -3x) * (1 + x) -8x + 6x2 + -1(1(1 + x) + -3x * (1 + x)) = -2 -8x + 6x2 + -1((1 * 1 + x * 1) + -3x * (1 + x)) = -2 -8x + 6x2 + -1((1 + 1x) + -3x * (1 + x)) = -2 -8x + 6x2 + -1(1 + 1x + (1 * -3x + x * -3x)) = -2 -8x + 6x2 + -1(1 + 1x + (-3x + -3x2)) = -2 Combine like terms: 1x + -3x = -2x -8x + 6x2 + -1(1 + -2x + -3x2) = -2 -8x + 6x2 + (1 * -1 + -2x * -1 + -3x2 * -1) = -2 -8x + 6x2 + (-1 + 2x + 3x2) = -2 Reorder the terms: -1 + -8x + 2x + 6x2 + 3x2 = -2 Combine like terms: -8x + 2x = -6x -1 + -6x + 6x2 + 3x2 = -2 Combine like terms: 6x2 + 3x2 = 9x2 -1 + -6x + 9x2 = -2 Solving -1 + -6x + 9x2 = -2 Solving for variable 'x'. Reorder the terms: -1 + 2 + -6x + 9x2 = -2 + 2 Combine like terms: -1 + 2 = 1 1 + -6x + 9x2 = -2 + 2 Combine like terms: -2 + 2 = 0 1 + -6x + 9x2 = 0 Factor a trinomial. (1 + -3x)(1 + -3x) = 0Subproblem 1
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 = 0.3333333333Subproblem 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 = {0.3333333333, 0.3333333333}
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