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Simplifying (4x + 3)(x + -2) = (x + -6)(3x + 4) Reorder the terms: (3 + 4x)(x + -2) = (x + -6)(3x + 4) Reorder the terms: (3 + 4x)(-2 + x) = (x + -6)(3x + 4) Multiply (3 + 4x) * (-2 + x) (3(-2 + x) + 4x * (-2 + x)) = (x + -6)(3x + 4) ((-2 * 3 + x * 3) + 4x * (-2 + x)) = (x + -6)(3x + 4) ((-6 + 3x) + 4x * (-2 + x)) = (x + -6)(3x + 4) (-6 + 3x + (-2 * 4x + x * 4x)) = (x + -6)(3x + 4) (-6 + 3x + (-8x + 4x2)) = (x + -6)(3x + 4) Combine like terms: 3x + -8x = -5x (-6 + -5x + 4x2) = (x + -6)(3x + 4) Reorder the terms: -6 + -5x + 4x2 = (-6 + x)(3x + 4) Reorder the terms: -6 + -5x + 4x2 = (-6 + x)(4 + 3x) Multiply (-6 + x) * (4 + 3x) -6 + -5x + 4x2 = (-6(4 + 3x) + x(4 + 3x)) -6 + -5x + 4x2 = ((4 * -6 + 3x * -6) + x(4 + 3x)) -6 + -5x + 4x2 = ((-24 + -18x) + x(4 + 3x)) -6 + -5x + 4x2 = (-24 + -18x + (4 * x + 3x * x)) -6 + -5x + 4x2 = (-24 + -18x + (4x + 3x2)) Combine like terms: -18x + 4x = -14x -6 + -5x + 4x2 = (-24 + -14x + 3x2) Solving -6 + -5x + 4x2 = -24 + -14x + 3x2 Solving for variable 'x'. Reorder the terms: -6 + 24 + -5x + 14x + 4x2 + -3x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2 Combine like terms: -6 + 24 = 18 18 + -5x + 14x + 4x2 + -3x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2 Combine like terms: -5x + 14x = 9x 18 + 9x + 4x2 + -3x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 18 + 9x + 1x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2 Reorder the terms: 18 + 9x + 1x2 = -24 + 24 + -14x + 14x + 3x2 + -3x2 Combine like terms: -24 + 24 = 0 18 + 9x + 1x2 = 0 + -14x + 14x + 3x2 + -3x2 18 + 9x + 1x2 = -14x + 14x + 3x2 + -3x2 Combine like terms: -14x + 14x = 0 18 + 9x + 1x2 = 0 + 3x2 + -3x2 18 + 9x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 18 + 9x + 1x2 = 0 Factor a trinomial. (6 + x)(3 + x) = 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 + 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 = -3Solution
x = {-6, -3}
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