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Simplifying (3 + -3x)(3x + 1) = (3 + -3x)(14x + 2) Reorder the terms: (3 + -3x)(1 + 3x) = (3 + -3x)(14x + 2) Multiply (3 + -3x) * (1 + 3x) (3(1 + 3x) + -3x * (1 + 3x)) = (3 + -3x)(14x + 2) ((1 * 3 + 3x * 3) + -3x * (1 + 3x)) = (3 + -3x)(14x + 2) ((3 + 9x) + -3x * (1 + 3x)) = (3 + -3x)(14x + 2) (3 + 9x + (1 * -3x + 3x * -3x)) = (3 + -3x)(14x + 2) (3 + 9x + (-3x + -9x2)) = (3 + -3x)(14x + 2) Combine like terms: 9x + -3x = 6x (3 + 6x + -9x2) = (3 + -3x)(14x + 2) Reorder the terms: 3 + 6x + -9x2 = (3 + -3x)(2 + 14x) Multiply (3 + -3x) * (2 + 14x) 3 + 6x + -9x2 = (3(2 + 14x) + -3x * (2 + 14x)) 3 + 6x + -9x2 = ((2 * 3 + 14x * 3) + -3x * (2 + 14x)) 3 + 6x + -9x2 = ((6 + 42x) + -3x * (2 + 14x)) 3 + 6x + -9x2 = (6 + 42x + (2 * -3x + 14x * -3x)) 3 + 6x + -9x2 = (6 + 42x + (-6x + -42x2)) Combine like terms: 42x + -6x = 36x 3 + 6x + -9x2 = (6 + 36x + -42x2) Solving 3 + 6x + -9x2 = 6 + 36x + -42x2 Solving for variable 'x'. Reorder the terms: 3 + -6 + 6x + -36x + -9x2 + 42x2 = 6 + 36x + -42x2 + -6 + -36x + 42x2 Combine like terms: 3 + -6 = -3 -3 + 6x + -36x + -9x2 + 42x2 = 6 + 36x + -42x2 + -6 + -36x + 42x2 Combine like terms: 6x + -36x = -30x -3 + -30x + -9x2 + 42x2 = 6 + 36x + -42x2 + -6 + -36x + 42x2 Combine like terms: -9x2 + 42x2 = 33x2 -3 + -30x + 33x2 = 6 + 36x + -42x2 + -6 + -36x + 42x2 Reorder the terms: -3 + -30x + 33x2 = 6 + -6 + 36x + -36x + -42x2 + 42x2 Combine like terms: 6 + -6 = 0 -3 + -30x + 33x2 = 0 + 36x + -36x + -42x2 + 42x2 -3 + -30x + 33x2 = 36x + -36x + -42x2 + 42x2 Combine like terms: 36x + -36x = 0 -3 + -30x + 33x2 = 0 + -42x2 + 42x2 -3 + -30x + 33x2 = -42x2 + 42x2 Combine like terms: -42x2 + 42x2 = 0 -3 + -30x + 33x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -10x + 11x2) = 0 Factor a trinomial. 3((-1 + -11x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -11x)' equal to zero and attempt to solve: Simplifying -1 + -11x = 0 Solving -1 + -11x = 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 + -11x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11x = 0 + 1 -11x = 0 + 1 Combine like terms: 0 + 1 = 1 -11x = 1 Divide each side by '-11'. x = -0.09090909091 Simplifying x = -0.09090909091Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-0.09090909091, 1}
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