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