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Simplifying (5x + 9)(x + -2) = (4x + 7)(x + -3) Reorder the terms: (9 + 5x)(x + -2) = (4x + 7)(x + -3) Reorder the terms: (9 + 5x)(-2 + x) = (4x + 7)(x + -3) Multiply (9 + 5x) * (-2 + x) (9(-2 + x) + 5x * (-2 + x)) = (4x + 7)(x + -3) ((-2 * 9 + x * 9) + 5x * (-2 + x)) = (4x + 7)(x + -3) ((-18 + 9x) + 5x * (-2 + x)) = (4x + 7)(x + -3) (-18 + 9x + (-2 * 5x + x * 5x)) = (4x + 7)(x + -3) (-18 + 9x + (-10x + 5x2)) = (4x + 7)(x + -3) Combine like terms: 9x + -10x = -1x (-18 + -1x + 5x2) = (4x + 7)(x + -3) Reorder the terms: -18 + -1x + 5x2 = (7 + 4x)(x + -3) Reorder the terms: -18 + -1x + 5x2 = (7 + 4x)(-3 + x) Multiply (7 + 4x) * (-3 + x) -18 + -1x + 5x2 = (7(-3 + x) + 4x * (-3 + x)) -18 + -1x + 5x2 = ((-3 * 7 + x * 7) + 4x * (-3 + x)) -18 + -1x + 5x2 = ((-21 + 7x) + 4x * (-3 + x)) -18 + -1x + 5x2 = (-21 + 7x + (-3 * 4x + x * 4x)) -18 + -1x + 5x2 = (-21 + 7x + (-12x + 4x2)) Combine like terms: 7x + -12x = -5x -18 + -1x + 5x2 = (-21 + -5x + 4x2) Solving -18 + -1x + 5x2 = -21 + -5x + 4x2 Solving for variable 'x'. Reorder the terms: -18 + 21 + -1x + 5x + 5x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2 Combine like terms: -18 + 21 = 3 3 + -1x + 5x + 5x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2 Combine like terms: -1x + 5x = 4x 3 + 4x + 5x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 3 + 4x + 1x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2 Reorder the terms: 3 + 4x + 1x2 = -21 + 21 + -5x + 5x + 4x2 + -4x2 Combine like terms: -21 + 21 = 0 3 + 4x + 1x2 = 0 + -5x + 5x + 4x2 + -4x2 3 + 4x + 1x2 = -5x + 5x + 4x2 + -4x2 Combine like terms: -5x + 5x = 0 3 + 4x + 1x2 = 0 + 4x2 + -4x2 3 + 4x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 4x + 1x2 = 0 Factor a trinomial. (3 + x)(1 + x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-3, -1}
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