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Simplifying (2x + -1)(3x + -1) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 Reorder the terms: (-1 + 2x)(3x + -1) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 Reorder the terms: (-1 + 2x)(-1 + 3x) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 Multiply (-1 + 2x) * (-1 + 3x) (-1(-1 + 3x) + 2x * (-1 + 3x)) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 ((-1 * -1 + 3x * -1) + 2x * (-1 + 3x)) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 ((1 + -3x) + 2x * (-1 + 3x)) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 (1 + -3x + (-1 * 2x + 3x * 2x)) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 (1 + -3x + (-2x + 6x2)) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 Combine like terms: -3x + -2x = -5x (1 + -5x + 6x2) + -1(2 + -4x)(x + 1) + (5x + 1)(x + 5) = 0 Reorder the terms: 1 + -5x + 6x2 + -1(2 + -4x)(1 + x) + (5x + 1)(x + 5) = 0 Multiply (2 + -4x) * (1 + x) 1 + -5x + 6x2 + -1(2(1 + x) + -4x * (1 + x)) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + -1((1 * 2 + x * 2) + -4x * (1 + x)) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + -1((2 + 2x) + -4x * (1 + x)) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + -1(2 + 2x + (1 * -4x + x * -4x)) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + -1(2 + 2x + (-4x + -4x2)) + (5x + 1)(x + 5) = 0 Combine like terms: 2x + -4x = -2x 1 + -5x + 6x2 + -1(2 + -2x + -4x2) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + (2 * -1 + -2x * -1 + -4x2 * -1) + (5x + 1)(x + 5) = 0 1 + -5x + 6x2 + (-2 + 2x + 4x2) + (5x + 1)(x + 5) = 0 Reorder the terms: 1 + -5x + 6x2 + -2 + 2x + 4x2 + (1 + 5x)(x + 5) = 0 Reorder the terms: 1 + -5x + 6x2 + -2 + 2x + 4x2 + (1 + 5x)(5 + x) = 0 Multiply (1 + 5x) * (5 + x) 1 + -5x + 6x2 + -2 + 2x + 4x2 + (1(5 + x) + 5x * (5 + x)) = 0 1 + -5x + 6x2 + -2 + 2x + 4x2 + ((5 * 1 + x * 1) + 5x * (5 + x)) = 0 1 + -5x + 6x2 + -2 + 2x + 4x2 + ((5 + 1x) + 5x * (5 + x)) = 0 1 + -5x + 6x2 + -2 + 2x + 4x2 + (5 + 1x + (5 * 5x + x * 5x)) = 0 1 + -5x + 6x2 + -2 + 2x + 4x2 + (5 + 1x + (25x + 5x2)) = 0 Combine like terms: 1x + 25x = 26x 1 + -5x + 6x2 + -2 + 2x + 4x2 + (5 + 26x + 5x2) = 0 Reorder the terms: 1 + -2 + 5 + -5x + 2x + 26x + 6x2 + 4x2 + 5x2 = 0 Combine like terms: 1 + -2 = -1 -1 + 5 + -5x + 2x + 26x + 6x2 + 4x2 + 5x2 = 0 Combine like terms: -1 + 5 = 4 4 + -5x + 2x + 26x + 6x2 + 4x2 + 5x2 = 0 Combine like terms: -5x + 2x = -3x 4 + -3x + 26x + 6x2 + 4x2 + 5x2 = 0 Combine like terms: -3x + 26x = 23x 4 + 23x + 6x2 + 4x2 + 5x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 4 + 23x + 10x2 + 5x2 = 0 Combine like terms: 10x2 + 5x2 = 15x2 4 + 23x + 15x2 = 0 Solving 4 + 23x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (4 + 3x)(1 + 5x) = 0Subproblem 1
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 2
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 = -0.2Solution
x = {-1.333333333, -0.2}
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