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Simplifying (x + 1)(2x + 3) + (x + 1)(5x + -4) = 0 Reorder the terms: (1 + x)(2x + 3) + (x + 1)(5x + -4) = 0 Reorder the terms: (1 + x)(3 + 2x) + (x + 1)(5x + -4) = 0 Multiply (1 + x) * (3 + 2x) (1(3 + 2x) + x(3 + 2x)) + (x + 1)(5x + -4) = 0 ((3 * 1 + 2x * 1) + x(3 + 2x)) + (x + 1)(5x + -4) = 0 ((3 + 2x) + x(3 + 2x)) + (x + 1)(5x + -4) = 0 (3 + 2x + (3 * x + 2x * x)) + (x + 1)(5x + -4) = 0 (3 + 2x + (3x + 2x2)) + (x + 1)(5x + -4) = 0 Combine like terms: 2x + 3x = 5x (3 + 5x + 2x2) + (x + 1)(5x + -4) = 0 Reorder the terms: 3 + 5x + 2x2 + (1 + x)(5x + -4) = 0 Reorder the terms: 3 + 5x + 2x2 + (1 + x)(-4 + 5x) = 0 Multiply (1 + x) * (-4 + 5x) 3 + 5x + 2x2 + (1(-4 + 5x) + x(-4 + 5x)) = 0 3 + 5x + 2x2 + ((-4 * 1 + 5x * 1) + x(-4 + 5x)) = 0 3 + 5x + 2x2 + ((-4 + 5x) + x(-4 + 5x)) = 0 3 + 5x + 2x2 + (-4 + 5x + (-4 * x + 5x * x)) = 0 3 + 5x + 2x2 + (-4 + 5x + (-4x + 5x2)) = 0 Combine like terms: 5x + -4x = 1x 3 + 5x + 2x2 + (-4 + 1x + 5x2) = 0 Reorder the terms: 3 + -4 + 5x + 1x + 2x2 + 5x2 = 0 Combine like terms: 3 + -4 = -1 -1 + 5x + 1x + 2x2 + 5x2 = 0 Combine like terms: 5x + 1x = 6x -1 + 6x + 2x2 + 5x2 = 0 Combine like terms: 2x2 + 5x2 = 7x2 -1 + 6x + 7x2 = 0 Solving -1 + 6x + 7x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(1 + -7x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Solution
x = {-1, 0.1428571429}
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