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Simplifying (x + 5)(x + -3) = (2x + 3)(x + -3) Reorder the terms: (5 + x)(x + -3) = (2x + 3)(x + -3) Reorder the terms: (5 + x)(-3 + x) = (2x + 3)(x + -3) Multiply (5 + x) * (-3 + x) (5(-3 + x) + x(-3 + x)) = (2x + 3)(x + -3) ((-3 * 5 + x * 5) + x(-3 + x)) = (2x + 3)(x + -3) ((-15 + 5x) + x(-3 + x)) = (2x + 3)(x + -3) (-15 + 5x + (-3 * x + x * x)) = (2x + 3)(x + -3) (-15 + 5x + (-3x + x2)) = (2x + 3)(x + -3) Combine like terms: 5x + -3x = 2x (-15 + 2x + x2) = (2x + 3)(x + -3) Reorder the terms: -15 + 2x + x2 = (3 + 2x)(x + -3) Reorder the terms: -15 + 2x + x2 = (3 + 2x)(-3 + x) Multiply (3 + 2x) * (-3 + x) -15 + 2x + x2 = (3(-3 + x) + 2x * (-3 + x)) -15 + 2x + x2 = ((-3 * 3 + x * 3) + 2x * (-3 + x)) -15 + 2x + x2 = ((-9 + 3x) + 2x * (-3 + x)) -15 + 2x + x2 = (-9 + 3x + (-3 * 2x + x * 2x)) -15 + 2x + x2 = (-9 + 3x + (-6x + 2x2)) Combine like terms: 3x + -6x = -3x -15 + 2x + x2 = (-9 + -3x + 2x2) Solving -15 + 2x + x2 = -9 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -15 + 9 + 2x + 3x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Combine like terms: -15 + 9 = -6 -6 + 2x + 3x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Combine like terms: 2x + 3x = 5x -6 + 5x + x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -6 + 5x + -1x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Reorder the terms: -6 + 5x + -1x2 = -9 + 9 + -3x + 3x + 2x2 + -2x2 Combine like terms: -9 + 9 = 0 -6 + 5x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2 -6 + 5x + -1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 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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