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Simplifying (x + 3)(x + -3) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 Reorder the terms: (3 + x)(x + -3) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 Reorder the terms: (3 + x)(-3 + x) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 Multiply (3 + x) * (-3 + x) (3(-3 + x) + x(-3 + x)) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 ((-3 * 3 + x * 3) + x(-3 + x)) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 ((-9 + 3x) + x(-3 + x)) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 (-9 + 3x + (-3 * x + x * x)) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 (-9 + 3x + (-3x + x2)) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 Combine like terms: 3x + -3x = 0 (-9 + 0 + x2) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 (-9 + x2) + (x + -3)(5x + -1) + -1(x + -3)(2x + 3) = 0 Reorder the terms: -9 + x2 + (-3 + x)(5x + -1) + -1(x + -3)(2x + 3) = 0 Reorder the terms: -9 + x2 + (-3 + x)(-1 + 5x) + -1(x + -3)(2x + 3) = 0 Multiply (-3 + x) * (-1 + 5x) -9 + x2 + (-3(-1 + 5x) + x(-1 + 5x)) + -1(x + -3)(2x + 3) = 0 -9 + x2 + ((-1 * -3 + 5x * -3) + x(-1 + 5x)) + -1(x + -3)(2x + 3) = 0 -9 + x2 + ((3 + -15x) + x(-1 + 5x)) + -1(x + -3)(2x + 3) = 0 -9 + x2 + (3 + -15x + (-1 * x + 5x * x)) + -1(x + -3)(2x + 3) = 0 -9 + x2 + (3 + -15x + (-1x + 5x2)) + -1(x + -3)(2x + 3) = 0 Combine like terms: -15x + -1x = -16x -9 + x2 + (3 + -16x + 5x2) + -1(x + -3)(2x + 3) = 0 Reorder the terms: -9 + x2 + 3 + -16x + 5x2 + -1(-3 + x)(2x + 3) = 0 Reorder the terms: -9 + x2 + 3 + -16x + 5x2 + -1(-3 + x)(3 + 2x) = 0 Multiply (-3 + x) * (3 + 2x) -9 + x2 + 3 + -16x + 5x2 + -1(-3(3 + 2x) + x(3 + 2x)) = 0 -9 + x2 + 3 + -16x + 5x2 + -1((3 * -3 + 2x * -3) + x(3 + 2x)) = 0 -9 + x2 + 3 + -16x + 5x2 + -1((-9 + -6x) + x(3 + 2x)) = 0 -9 + x2 + 3 + -16x + 5x2 + -1(-9 + -6x + (3 * x + 2x * x)) = 0 -9 + x2 + 3 + -16x + 5x2 + -1(-9 + -6x + (3x + 2x2)) = 0 Combine like terms: -6x + 3x = -3x -9 + x2 + 3 + -16x + 5x2 + -1(-9 + -3x + 2x2) = 0 -9 + x2 + 3 + -16x + 5x2 + (-9 * -1 + -3x * -1 + 2x2 * -1) = 0 -9 + x2 + 3 + -16x + 5x2 + (9 + 3x + -2x2) = 0 Reorder the terms: -9 + 3 + 9 + -16x + 3x + x2 + 5x2 + -2x2 = 0 Combine like terms: -9 + 3 = -6 -6 + 9 + -16x + 3x + x2 + 5x2 + -2x2 = 0 Combine like terms: -6 + 9 = 3 3 + -16x + 3x + x2 + 5x2 + -2x2 = 0 Combine like terms: -16x + 3x = -13x 3 + -13x + x2 + 5x2 + -2x2 = 0 Combine like terms: x2 + 5x2 = 6x2 3 + -13x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 3 + -13x + 4x2 = 0 Solving 3 + -13x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0.25, 3}
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