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Simplifying (5x + -6)(x + 3) = (x + 2)(4x + -3) Reorder the terms: (-6 + 5x)(x + 3) = (x + 2)(4x + -3) Reorder the terms: (-6 + 5x)(3 + x) = (x + 2)(4x + -3) Multiply (-6 + 5x) * (3 + x) (-6(3 + x) + 5x * (3 + x)) = (x + 2)(4x + -3) ((3 * -6 + x * -6) + 5x * (3 + x)) = (x + 2)(4x + -3) ((-18 + -6x) + 5x * (3 + x)) = (x + 2)(4x + -3) (-18 + -6x + (3 * 5x + x * 5x)) = (x + 2)(4x + -3) (-18 + -6x + (15x + 5x2)) = (x + 2)(4x + -3) Combine like terms: -6x + 15x = 9x (-18 + 9x + 5x2) = (x + 2)(4x + -3) Reorder the terms: -18 + 9x + 5x2 = (2 + x)(4x + -3) Reorder the terms: -18 + 9x + 5x2 = (2 + x)(-3 + 4x) Multiply (2 + x) * (-3 + 4x) -18 + 9x + 5x2 = (2(-3 + 4x) + x(-3 + 4x)) -18 + 9x + 5x2 = ((-3 * 2 + 4x * 2) + x(-3 + 4x)) -18 + 9x + 5x2 = ((-6 + 8x) + x(-3 + 4x)) -18 + 9x + 5x2 = (-6 + 8x + (-3 * x + 4x * x)) -18 + 9x + 5x2 = (-6 + 8x + (-3x + 4x2)) Combine like terms: 8x + -3x = 5x -18 + 9x + 5x2 = (-6 + 5x + 4x2) Solving -18 + 9x + 5x2 = -6 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: -18 + 6 + 9x + -5x + 5x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: -18 + 6 = -12 -12 + 9x + -5x + 5x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: 9x + -5x = 4x -12 + 4x + 5x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 -12 + 4x + 1x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2 Reorder the terms: -12 + 4x + 1x2 = -6 + 6 + 5x + -5x + 4x2 + -4x2 Combine like terms: -6 + 6 = 0 -12 + 4x + 1x2 = 0 + 5x + -5x + 4x2 + -4x2 -12 + 4x + 1x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 -12 + 4x + 1x2 = 0 + 4x2 + -4x2 -12 + 4x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12 + 4x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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 = {-6, 2}
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