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Simplifying (2x + -5x + 5)(x + 4x + -3) + (2x + -5x + 5)(x + 4x + -3) = 0 Reorder the terms: (5 + 2x + -5x)(x + 4x + -3) + (2x + -5x + 5)(x + 4x + -3) = 0 Combine like terms: 2x + -5x = -3x (5 + -3x)(x + 4x + -3) + (2x + -5x + 5)(x + 4x + -3) = 0 Reorder the terms: (5 + -3x)(-3 + x + 4x) + (2x + -5x + 5)(x + 4x + -3) = 0 Combine like terms: x + 4x = 5x (5 + -3x)(-3 + 5x) + (2x + -5x + 5)(x + 4x + -3) = 0 Multiply (5 + -3x) * (-3 + 5x) (5(-3 + 5x) + -3x * (-3 + 5x)) + (2x + -5x + 5)(x + 4x + -3) = 0 ((-3 * 5 + 5x * 5) + -3x * (-3 + 5x)) + (2x + -5x + 5)(x + 4x + -3) = 0 ((-15 + 25x) + -3x * (-3 + 5x)) + (2x + -5x + 5)(x + 4x + -3) = 0 (-15 + 25x + (-3 * -3x + 5x * -3x)) + (2x + -5x + 5)(x + 4x + -3) = 0 (-15 + 25x + (9x + -15x2)) + (2x + -5x + 5)(x + 4x + -3) = 0 Combine like terms: 25x + 9x = 34x (-15 + 34x + -15x2) + (2x + -5x + 5)(x + 4x + -3) = 0 Reorder the terms: -15 + 34x + -15x2 + (5 + 2x + -5x)(x + 4x + -3) = 0 Combine like terms: 2x + -5x = -3x -15 + 34x + -15x2 + (5 + -3x)(x + 4x + -3) = 0 Reorder the terms: -15 + 34x + -15x2 + (5 + -3x)(-3 + x + 4x) = 0 Combine like terms: x + 4x = 5x -15 + 34x + -15x2 + (5 + -3x)(-3 + 5x) = 0 Multiply (5 + -3x) * (-3 + 5x) -15 + 34x + -15x2 + (5(-3 + 5x) + -3x * (-3 + 5x)) = 0 -15 + 34x + -15x2 + ((-3 * 5 + 5x * 5) + -3x * (-3 + 5x)) = 0 -15 + 34x + -15x2 + ((-15 + 25x) + -3x * (-3 + 5x)) = 0 -15 + 34x + -15x2 + (-15 + 25x + (-3 * -3x + 5x * -3x)) = 0 -15 + 34x + -15x2 + (-15 + 25x + (9x + -15x2)) = 0 Combine like terms: 25x + 9x = 34x -15 + 34x + -15x2 + (-15 + 34x + -15x2) = 0 Reorder the terms: -15 + -15 + 34x + 34x + -15x2 + -15x2 = 0 Combine like terms: -15 + -15 = -30 -30 + 34x + 34x + -15x2 + -15x2 = 0 Combine like terms: 34x + 34x = 68x -30 + 68x + -15x2 + -15x2 = 0 Combine like terms: -15x2 + -15x2 = -30x2 -30 + 68x + -30x2 = 0 Solving -30 + 68x + -30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 34x + -15x2) = 0 Factor a trinomial. 2((-5 + 3x)(3 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Divide each side by '3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {1.666666667, 0.6}
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