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Simplifying (3x + -1)(2x + -5) + -1(3x + -1)(5x + 3) = 0 Reorder the terms: (-1 + 3x)(2x + -5) + -1(3x + -1)(5x + 3) = 0 Reorder the terms: (-1 + 3x)(-5 + 2x) + -1(3x + -1)(5x + 3) = 0 Multiply (-1 + 3x) * (-5 + 2x) (-1(-5 + 2x) + 3x * (-5 + 2x)) + -1(3x + -1)(5x + 3) = 0 ((-5 * -1 + 2x * -1) + 3x * (-5 + 2x)) + -1(3x + -1)(5x + 3) = 0 ((5 + -2x) + 3x * (-5 + 2x)) + -1(3x + -1)(5x + 3) = 0 (5 + -2x + (-5 * 3x + 2x * 3x)) + -1(3x + -1)(5x + 3) = 0 (5 + -2x + (-15x + 6x2)) + -1(3x + -1)(5x + 3) = 0 Combine like terms: -2x + -15x = -17x (5 + -17x + 6x2) + -1(3x + -1)(5x + 3) = 0 Reorder the terms: 5 + -17x + 6x2 + -1(-1 + 3x)(5x + 3) = 0 Reorder the terms: 5 + -17x + 6x2 + -1(-1 + 3x)(3 + 5x) = 0 Multiply (-1 + 3x) * (3 + 5x) 5 + -17x + 6x2 + -1(-1(3 + 5x) + 3x * (3 + 5x)) = 0 5 + -17x + 6x2 + -1((3 * -1 + 5x * -1) + 3x * (3 + 5x)) = 0 5 + -17x + 6x2 + -1((-3 + -5x) + 3x * (3 + 5x)) = 0 5 + -17x + 6x2 + -1(-3 + -5x + (3 * 3x + 5x * 3x)) = 0 5 + -17x + 6x2 + -1(-3 + -5x + (9x + 15x2)) = 0 Combine like terms: -5x + 9x = 4x 5 + -17x + 6x2 + -1(-3 + 4x + 15x2) = 0 5 + -17x + 6x2 + (-3 * -1 + 4x * -1 + 15x2 * -1) = 0 5 + -17x + 6x2 + (3 + -4x + -15x2) = 0 Reorder the terms: 5 + 3 + -17x + -4x + 6x2 + -15x2 = 0 Combine like terms: 5 + 3 = 8 8 + -17x + -4x + 6x2 + -15x2 = 0 Combine like terms: -17x + -4x = -21x 8 + -21x + 6x2 + -15x2 = 0 Combine like terms: 6x2 + -15x2 = -9x2 8 + -21x + -9x2 = 0 Solving 8 + -21x + -9x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -3x)(8 + 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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Divide each side by '3'. x = -2.666666667 Simplifying x = -2.666666667Solution
x = {0.3333333333, -2.666666667}
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