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Simplifying (x + 2)(x + 4) + 2(x + 2)(x + -3) = 0 Reorder the terms: (2 + x)(x + 4) + 2(x + 2)(x + -3) = 0 Reorder the terms: (2 + x)(4 + x) + 2(x + 2)(x + -3) = 0 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) + 2(x + 2)(x + -3) = 0 ((4 * 2 + x * 2) + x(4 + x)) + 2(x + 2)(x + -3) = 0 ((8 + 2x) + x(4 + x)) + 2(x + 2)(x + -3) = 0 (8 + 2x + (4 * x + x * x)) + 2(x + 2)(x + -3) = 0 (8 + 2x + (4x + x2)) + 2(x + 2)(x + -3) = 0 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) + 2(x + 2)(x + -3) = 0 Reorder the terms: 8 + 6x + x2 + 2(2 + x)(x + -3) = 0 Reorder the terms: 8 + 6x + x2 + 2(2 + x)(-3 + x) = 0 Multiply (2 + x) * (-3 + x) 8 + 6x + x2 + 2(2(-3 + x) + x(-3 + x)) = 0 8 + 6x + x2 + 2((-3 * 2 + x * 2) + x(-3 + x)) = 0 8 + 6x + x2 + 2((-6 + 2x) + x(-3 + x)) = 0 8 + 6x + x2 + 2(-6 + 2x + (-3 * x + x * x)) = 0 8 + 6x + x2 + 2(-6 + 2x + (-3x + x2)) = 0 Combine like terms: 2x + -3x = -1x 8 + 6x + x2 + 2(-6 + -1x + x2) = 0 8 + 6x + x2 + (-6 * 2 + -1x * 2 + x2 * 2) = 0 8 + 6x + x2 + (-12 + -2x + 2x2) = 0 Reorder the terms: 8 + -12 + 6x + -2x + x2 + 2x2 = 0 Combine like terms: 8 + -12 = -4 -4 + 6x + -2x + x2 + 2x2 = 0 Combine like terms: 6x + -2x = 4x -4 + 4x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -4 + 4x + 3x2 = 0 Solving -4 + 4x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + -1x)(2 + -3x) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-2, 0.6666666667}
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