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