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Simplifying (3x + -1)(3x + -1) = (2x + 3)(2x + 3) Reorder the terms: (-1 + 3x)(3x + -1) = (2x + 3)(2x + 3) Reorder the terms: (-1 + 3x)(-1 + 3x) = (2x + 3)(2x + 3) Multiply (-1 + 3x) * (-1 + 3x) (-1(-1 + 3x) + 3x * (-1 + 3x)) = (2x + 3)(2x + 3) ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = (2x + 3)(2x + 3) ((1 + -3x) + 3x * (-1 + 3x)) = (2x + 3)(2x + 3) (1 + -3x + (-1 * 3x + 3x * 3x)) = (2x + 3)(2x + 3) (1 + -3x + (-3x + 9x2)) = (2x + 3)(2x + 3) Combine like terms: -3x + -3x = -6x (1 + -6x + 9x2) = (2x + 3)(2x + 3) Reorder the terms: 1 + -6x + 9x2 = (3 + 2x)(2x + 3) Reorder the terms: 1 + -6x + 9x2 = (3 + 2x)(3 + 2x) Multiply (3 + 2x) * (3 + 2x) 1 + -6x + 9x2 = (3(3 + 2x) + 2x * (3 + 2x)) 1 + -6x + 9x2 = ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) 1 + -6x + 9x2 = ((9 + 6x) + 2x * (3 + 2x)) 1 + -6x + 9x2 = (9 + 6x + (3 * 2x + 2x * 2x)) 1 + -6x + 9x2 = (9 + 6x + (6x + 4x2)) Combine like terms: 6x + 6x = 12x 1 + -6x + 9x2 = (9 + 12x + 4x2) Solving 1 + -6x + 9x2 = 9 + 12x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + -9 + -6x + -12x + 9x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 1 + -9 = -8 -8 + -6x + -12x + 9x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: -6x + -12x = -18x -8 + -18x + 9x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -8 + -18x + 5x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Reorder the terms: -8 + -18x + 5x2 = 9 + -9 + 12x + -12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -8 + -18x + 5x2 = 0 + 12x + -12x + 4x2 + -4x2 -8 + -18x + 5x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -8 + -18x + 5x2 = 0 + 4x2 + -4x2 -8 + -18x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8 + -18x + 5x2 = 0 Factor a trinomial. (-2 + -5x)(4 + -1x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.4, 4}
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