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Simplifying x + (2x + 3)(x + -2) = 2(x + -3)(x + 4) Reorder the terms: x + (3 + 2x)(x + -2) = 2(x + -3)(x + 4) Reorder the terms: x + (3 + 2x)(-2 + x) = 2(x + -3)(x + 4) Multiply (3 + 2x) * (-2 + x) x + (3(-2 + x) + 2x * (-2 + x)) = 2(x + -3)(x + 4) x + ((-2 * 3 + x * 3) + 2x * (-2 + x)) = 2(x + -3)(x + 4) x + ((-6 + 3x) + 2x * (-2 + x)) = 2(x + -3)(x + 4) x + (-6 + 3x + (-2 * 2x + x * 2x)) = 2(x + -3)(x + 4) x + (-6 + 3x + (-4x + 2x2)) = 2(x + -3)(x + 4) Combine like terms: 3x + -4x = -1x x + (-6 + -1x + 2x2) = 2(x + -3)(x + 4) Reorder the terms: -6 + x + -1x + 2x2 = 2(x + -3)(x + 4) Combine like terms: x + -1x = 0 -6 + 0 + 2x2 = 2(x + -3)(x + 4) -6 + 2x2 = 2(x + -3)(x + 4) Reorder the terms: -6 + 2x2 = 2(-3 + x)(x + 4) Reorder the terms: -6 + 2x2 = 2(-3 + x)(4 + x) Multiply (-3 + x) * (4 + x) -6 + 2x2 = 2(-3(4 + x) + x(4 + x)) -6 + 2x2 = 2((4 * -3 + x * -3) + x(4 + x)) -6 + 2x2 = 2((-12 + -3x) + x(4 + x)) -6 + 2x2 = 2(-12 + -3x + (4 * x + x * x)) -6 + 2x2 = 2(-12 + -3x + (4x + x2)) Combine like terms: -3x + 4x = 1x -6 + 2x2 = 2(-12 + 1x + x2) -6 + 2x2 = (-12 * 2 + 1x * 2 + x2 * 2) -6 + 2x2 = (-24 + 2x + 2x2) Add '-2x2' to each side of the equation. -6 + 2x2 + -2x2 = -24 + 2x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 0 = -24 + 2x + 2x2 + -2x2 -6 = -24 + 2x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 = -24 + 2x + 0 -6 = -24 + 2x Solving -6 = -24 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -6 + -2x = -24 + 2x + -2x Combine like terms: 2x + -2x = 0 -6 + -2x = -24 + 0 -6 + -2x = -24 Add '6' to each side of the equation. -6 + 6 + -2x = -24 + 6 Combine like terms: -6 + 6 = 0 0 + -2x = -24 + 6 -2x = -24 + 6 Combine like terms: -24 + 6 = -18 -2x = -18 Divide each side by '-2'. x = 9 Simplifying x = 9
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