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Simplifying (3x)(3x) + -1 = (3x + -1)(2x + 5) Remove parenthesis around (3x) 3x(3x) + -1 = (3x + -1)(2x + 5) Remove parenthesis around (3x) 3x * 3x + -1 = (3x + -1)(2x + 5) Reorder the terms for easier multiplication: 3 * 3x * x + -1 = (3x + -1)(2x + 5) Multiply 3 * 3 9x * x + -1 = (3x + -1)(2x + 5) Multiply x * x 9x2 + -1 = (3x + -1)(2x + 5) Reorder the terms: -1 + 9x2 = (3x + -1)(2x + 5) Reorder the terms: -1 + 9x2 = (-1 + 3x)(2x + 5) Reorder the terms: -1 + 9x2 = (-1 + 3x)(5 + 2x) Multiply (-1 + 3x) * (5 + 2x) -1 + 9x2 = (-1(5 + 2x) + 3x * (5 + 2x)) -1 + 9x2 = ((5 * -1 + 2x * -1) + 3x * (5 + 2x)) -1 + 9x2 = ((-5 + -2x) + 3x * (5 + 2x)) -1 + 9x2 = (-5 + -2x + (5 * 3x + 2x * 3x)) -1 + 9x2 = (-5 + -2x + (15x + 6x2)) Combine like terms: -2x + 15x = 13x -1 + 9x2 = (-5 + 13x + 6x2) Solving -1 + 9x2 = -5 + 13x + 6x2 Solving for variable 'x'. Reorder the terms: -1 + 5 + -13x + 9x2 + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Combine like terms: -1 + 5 = 4 4 + -13x + 9x2 + -6x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Combine like terms: 9x2 + -6x2 = 3x2 4 + -13x + 3x2 = -5 + 13x + 6x2 + 5 + -13x + -6x2 Reorder the terms: 4 + -13x + 3x2 = -5 + 5 + 13x + -13x + 6x2 + -6x2 Combine like terms: -5 + 5 = 0 4 + -13x + 3x2 = 0 + 13x + -13x + 6x2 + -6x2 4 + -13x + 3x2 = 13x + -13x + 6x2 + -6x2 Combine like terms: 13x + -13x = 0 4 + -13x + 3x2 = 0 + 6x2 + -6x2 4 + -13x + 3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 4 + -13x + 3x2 = 0 Factor a trinomial. (1 + -3x)(4 + -1x) = 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 '(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 = {0.3333333333, 4}
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