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Simplifying (-4x + -1)(-2x + -5) = (-2x + -5)(3x + 1) Reorder the terms: (-1 + -4x)(-2x + -5) = (-2x + -5)(3x + 1) Reorder the terms: (-1 + -4x)(-5 + -2x) = (-2x + -5)(3x + 1) Multiply (-1 + -4x) * (-5 + -2x) (-1(-5 + -2x) + -4x * (-5 + -2x)) = (-2x + -5)(3x + 1) ((-5 * -1 + -2x * -1) + -4x * (-5 + -2x)) = (-2x + -5)(3x + 1) ((5 + 2x) + -4x * (-5 + -2x)) = (-2x + -5)(3x + 1) (5 + 2x + (-5 * -4x + -2x * -4x)) = (-2x + -5)(3x + 1) (5 + 2x + (20x + 8x2)) = (-2x + -5)(3x + 1) Combine like terms: 2x + 20x = 22x (5 + 22x + 8x2) = (-2x + -5)(3x + 1) Reorder the terms: 5 + 22x + 8x2 = (-5 + -2x)(3x + 1) Reorder the terms: 5 + 22x + 8x2 = (-5 + -2x)(1 + 3x) Multiply (-5 + -2x) * (1 + 3x) 5 + 22x + 8x2 = (-5(1 + 3x) + -2x * (1 + 3x)) 5 + 22x + 8x2 = ((1 * -5 + 3x * -5) + -2x * (1 + 3x)) 5 + 22x + 8x2 = ((-5 + -15x) + -2x * (1 + 3x)) 5 + 22x + 8x2 = (-5 + -15x + (1 * -2x + 3x * -2x)) 5 + 22x + 8x2 = (-5 + -15x + (-2x + -6x2)) Combine like terms: -15x + -2x = -17x 5 + 22x + 8x2 = (-5 + -17x + -6x2) Solving 5 + 22x + 8x2 = -5 + -17x + -6x2 Solving for variable 'x'. Reorder the terms: 5 + 5 + 22x + 17x + 8x2 + 6x2 = -5 + -17x + -6x2 + 5 + 17x + 6x2 Combine like terms: 5 + 5 = 10 10 + 22x + 17x + 8x2 + 6x2 = -5 + -17x + -6x2 + 5 + 17x + 6x2 Combine like terms: 22x + 17x = 39x 10 + 39x + 8x2 + 6x2 = -5 + -17x + -6x2 + 5 + 17x + 6x2 Combine like terms: 8x2 + 6x2 = 14x2 10 + 39x + 14x2 = -5 + -17x + -6x2 + 5 + 17x + 6x2 Reorder the terms: 10 + 39x + 14x2 = -5 + 5 + -17x + 17x + -6x2 + 6x2 Combine like terms: -5 + 5 = 0 10 + 39x + 14x2 = 0 + -17x + 17x + -6x2 + 6x2 10 + 39x + 14x2 = -17x + 17x + -6x2 + 6x2 Combine like terms: -17x + 17x = 0 10 + 39x + 14x2 = 0 + -6x2 + 6x2 10 + 39x + 14x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 10 + 39x + 14x2 = 0 Factor a trinomial. (5 + 2x)(2 + 7x) = 0Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Divide each side by '7'. x = -0.2857142857 Simplifying x = -0.2857142857Solution
x = {-2.5, -0.2857142857}
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