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Simplifying (x + 1)(4x + -3) = 2(x + 1)(2x + 3) Reorder the terms: (1 + x)(4x + -3) = 2(x + 1)(2x + 3) Reorder the terms: (1 + x)(-3 + 4x) = 2(x + 1)(2x + 3) Multiply (1 + x) * (-3 + 4x) (1(-3 + 4x) + x(-3 + 4x)) = 2(x + 1)(2x + 3) ((-3 * 1 + 4x * 1) + x(-3 + 4x)) = 2(x + 1)(2x + 3) ((-3 + 4x) + x(-3 + 4x)) = 2(x + 1)(2x + 3) (-3 + 4x + (-3 * x + 4x * x)) = 2(x + 1)(2x + 3) (-3 + 4x + (-3x + 4x2)) = 2(x + 1)(2x + 3) Combine like terms: 4x + -3x = 1x (-3 + 1x + 4x2) = 2(x + 1)(2x + 3) Reorder the terms: -3 + 1x + 4x2 = 2(1 + x)(2x + 3) Reorder the terms: -3 + 1x + 4x2 = 2(1 + x)(3 + 2x) Multiply (1 + x) * (3 + 2x) -3 + 1x + 4x2 = 2(1(3 + 2x) + x(3 + 2x)) -3 + 1x + 4x2 = 2((3 * 1 + 2x * 1) + x(3 + 2x)) -3 + 1x + 4x2 = 2((3 + 2x) + x(3 + 2x)) -3 + 1x + 4x2 = 2(3 + 2x + (3 * x + 2x * x)) -3 + 1x + 4x2 = 2(3 + 2x + (3x + 2x2)) Combine like terms: 2x + 3x = 5x -3 + 1x + 4x2 = 2(3 + 5x + 2x2) -3 + 1x + 4x2 = (3 * 2 + 5x * 2 + 2x2 * 2) -3 + 1x + 4x2 = (6 + 10x + 4x2) Add '-4x2' to each side of the equation. -3 + 1x + 4x2 + -4x2 = 6 + 10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 1x + 0 = 6 + 10x + 4x2 + -4x2 -3 + 1x = 6 + 10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 1x = 6 + 10x + 0 -3 + 1x = 6 + 10x Solving -3 + 1x = 6 + 10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. -3 + 1x + -10x = 6 + 10x + -10x Combine like terms: 1x + -10x = -9x -3 + -9x = 6 + 10x + -10x Combine like terms: 10x + -10x = 0 -3 + -9x = 6 + 0 -3 + -9x = 6 Add '3' to each side of the equation. -3 + 3 + -9x = 6 + 3 Combine like terms: -3 + 3 = 0 0 + -9x = 6 + 3 -9x = 6 + 3 Combine like terms: 6 + 3 = 9 -9x = 9 Divide each side by '-9'. x = -1 Simplifying x = -1
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