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Simplifying 2x(3x + -2) + -3x(3 + -1x) + 7x = (1 + -3x) + -1 Reorder the terms: 2x(-2 + 3x) + -3x(3 + -1x) + 7x = (1 + -3x) + -1 (-2 * 2x + 3x * 2x) + -3x(3 + -1x) + 7x = (1 + -3x) + -1 (-4x + 6x2) + -3x(3 + -1x) + 7x = (1 + -3x) + -1 -4x + 6x2 + (3 * -3x + -1x * -3x) + 7x = (1 + -3x) + -1 -4x + 6x2 + (-9x + 3x2) + 7x = (1 + -3x) + -1 Reorder the terms: -4x + -9x + 7x + 6x2 + 3x2 = (1 + -3x) + -1 Combine like terms: -4x + -9x = -13x -13x + 7x + 6x2 + 3x2 = (1 + -3x) + -1 Combine like terms: -13x + 7x = -6x -6x + 6x2 + 3x2 = (1 + -3x) + -1 Combine like terms: 6x2 + 3x2 = 9x2 -6x + 9x2 = (1 + -3x) + -1 Remove parenthesis around (1 + -3x) -6x + 9x2 = 1 + -3x + -1 Reorder the terms: -6x + 9x2 = 1 + -1 + -3x Combine like terms: 1 + -1 = 0 -6x + 9x2 = 0 + -3x -6x + 9x2 = -3x Solving -6x + 9x2 = -3x Solving for variable 'x'. Reorder the terms: -6x + 3x + 9x2 = -3x + 3x Combine like terms: -6x + 3x = -3x -3x + 9x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -3x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-1 + 3x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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, 0.3333333333}
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