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Simplifying (x + 2)(3x + -5) + (4x + -3)(3x + -5) = 0 Reorder the terms: (2 + x)(3x + -5) + (4x + -3)(3x + -5) = 0 Reorder the terms: (2 + x)(-5 + 3x) + (4x + -3)(3x + -5) = 0 Multiply (2 + x) * (-5 + 3x) (2(-5 + 3x) + x(-5 + 3x)) + (4x + -3)(3x + -5) = 0 ((-5 * 2 + 3x * 2) + x(-5 + 3x)) + (4x + -3)(3x + -5) = 0 ((-10 + 6x) + x(-5 + 3x)) + (4x + -3)(3x + -5) = 0 (-10 + 6x + (-5 * x + 3x * x)) + (4x + -3)(3x + -5) = 0 (-10 + 6x + (-5x + 3x2)) + (4x + -3)(3x + -5) = 0 Combine like terms: 6x + -5x = 1x (-10 + 1x + 3x2) + (4x + -3)(3x + -5) = 0 Reorder the terms: -10 + 1x + 3x2 + (-3 + 4x)(3x + -5) = 0 Reorder the terms: -10 + 1x + 3x2 + (-3 + 4x)(-5 + 3x) = 0 Multiply (-3 + 4x) * (-5 + 3x) -10 + 1x + 3x2 + (-3(-5 + 3x) + 4x * (-5 + 3x)) = 0 -10 + 1x + 3x2 + ((-5 * -3 + 3x * -3) + 4x * (-5 + 3x)) = 0 -10 + 1x + 3x2 + ((15 + -9x) + 4x * (-5 + 3x)) = 0 -10 + 1x + 3x2 + (15 + -9x + (-5 * 4x + 3x * 4x)) = 0 -10 + 1x + 3x2 + (15 + -9x + (-20x + 12x2)) = 0 Combine like terms: -9x + -20x = -29x -10 + 1x + 3x2 + (15 + -29x + 12x2) = 0 Reorder the terms: -10 + 15 + 1x + -29x + 3x2 + 12x2 = 0 Combine like terms: -10 + 15 = 5 5 + 1x + -29x + 3x2 + 12x2 = 0 Combine like terms: 1x + -29x = -28x 5 + -28x + 3x2 + 12x2 = 0 Combine like terms: 3x2 + 12x2 = 15x2 5 + -28x + 15x2 = 0 Solving 5 + -28x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -5x)(5 + -3x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
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 = 1.666666667Solution
x = {0.2, 1.666666667}
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