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