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Simplifying (x + 5)(x + -3) = (2x + 1)(x + -3) Reorder the terms: (5 + x)(x + -3) = (2x + 1)(x + -3) Reorder the terms: (5 + x)(-3 + x) = (2x + 1)(x + -3) Multiply (5 + x) * (-3 + x) (5(-3 + x) + x(-3 + x)) = (2x + 1)(x + -3) ((-3 * 5 + x * 5) + x(-3 + x)) = (2x + 1)(x + -3) ((-15 + 5x) + x(-3 + x)) = (2x + 1)(x + -3) (-15 + 5x + (-3 * x + x * x)) = (2x + 1)(x + -3) (-15 + 5x + (-3x + x2)) = (2x + 1)(x + -3) Combine like terms: 5x + -3x = 2x (-15 + 2x + x2) = (2x + 1)(x + -3) Reorder the terms: -15 + 2x + x2 = (1 + 2x)(x + -3) Reorder the terms: -15 + 2x + x2 = (1 + 2x)(-3 + x) Multiply (1 + 2x) * (-3 + x) -15 + 2x + x2 = (1(-3 + x) + 2x * (-3 + x)) -15 + 2x + x2 = ((-3 * 1 + x * 1) + 2x * (-3 + x)) -15 + 2x + x2 = ((-3 + 1x) + 2x * (-3 + x)) -15 + 2x + x2 = (-3 + 1x + (-3 * 2x + x * 2x)) -15 + 2x + x2 = (-3 + 1x + (-6x + 2x2)) Combine like terms: 1x + -6x = -5x -15 + 2x + x2 = (-3 + -5x + 2x2) Solving -15 + 2x + x2 = -3 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: -15 + 3 + 2x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: -15 + 3 = -12 -12 + 2x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: 2x + 5x = 7x -12 + 7x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -12 + 7x + -1x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Reorder the terms: -12 + 7x + -1x2 = -3 + 3 + -5x + 5x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 -12 + 7x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2 -12 + 7x + -1x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 -12 + 7x + -1x2 = 0 + 2x2 + -2x2 -12 + 7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 7x + -1x2 = 0 Factor a trinomial. (-4 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {4, 3}
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