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Simplifying (x + 6)(3x + -4) = (x + 2)(4x + -3) Reorder the terms: (6 + x)(3x + -4) = (x + 2)(4x + -3) Reorder the terms: (6 + x)(-4 + 3x) = (x + 2)(4x + -3) Multiply (6 + x) * (-4 + 3x) (6(-4 + 3x) + x(-4 + 3x)) = (x + 2)(4x + -3) ((-4 * 6 + 3x * 6) + x(-4 + 3x)) = (x + 2)(4x + -3) ((-24 + 18x) + x(-4 + 3x)) = (x + 2)(4x + -3) (-24 + 18x + (-4 * x + 3x * x)) = (x + 2)(4x + -3) (-24 + 18x + (-4x + 3x2)) = (x + 2)(4x + -3) Combine like terms: 18x + -4x = 14x (-24 + 14x + 3x2) = (x + 2)(4x + -3) Reorder the terms: -24 + 14x + 3x2 = (2 + x)(4x + -3) Reorder the terms: -24 + 14x + 3x2 = (2 + x)(-3 + 4x) Multiply (2 + x) * (-3 + 4x) -24 + 14x + 3x2 = (2(-3 + 4x) + x(-3 + 4x)) -24 + 14x + 3x2 = ((-3 * 2 + 4x * 2) + x(-3 + 4x)) -24 + 14x + 3x2 = ((-6 + 8x) + x(-3 + 4x)) -24 + 14x + 3x2 = (-6 + 8x + (-3 * x + 4x * x)) -24 + 14x + 3x2 = (-6 + 8x + (-3x + 4x2)) Combine like terms: 8x + -3x = 5x -24 + 14x + 3x2 = (-6 + 5x + 4x2) Solving -24 + 14x + 3x2 = -6 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: -24 + 6 + 14x + -5x + 3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: -24 + 6 = -18 -18 + 14x + -5x + 3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: 14x + -5x = 9x -18 + 9x + 3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 -18 + 9x + -1x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Reorder the terms: -18 + 9x + -1x2 = -6 + 6 + 5x + -5x + 4x2 + -4x2 Combine like terms: -6 + 6 = 0 -18 + 9x + -1x2 = 0 + 5x + -5x + 4x2 + -4x2 -18 + 9x + -1x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 -18 + 9x + -1x2 = 0 + 4x2 + -4x2 -18 + 9x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -18 + 9x + -1x2 = 0 Factor a trinomial. (-6 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 3}
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