Question

x(x+1) + (x+2)(x+3) = 42

Answer 1

Simplifying x(x + 1) + (x + 2)(x + 3) = 42 Reorder the terms: x(1 + x) + (x + 2)(x + 3) = 42 (1 * x + x * x) + (x + 2)(x + 3) = 42 (1x + x2) + (x + 2)(x + 3) = 42 Reorder the terms: 1x + x2 + (2 + x)(x + 3) = 42 Reorder the terms: 1x + x2 + (2 + x)(3 + x) = 42 Multiply (2 + x) * (3 + x) 1x + x2 + (2(3 + x) + x(3 + x)) = 42 1x + x2 + ((3 * 2 + x * 2) + x(3 + x)) = 42 1x + x2 + ((6 + 2x) + x(3 + x)) = 42 1x + x2 + (6 + 2x + (3 * x + x * x)) = 42 1x + x2 + (6 + 2x + (3x + x2)) = 42 Combine like terms: 2x + 3x = 5x 1x + x2 + (6 + 5x + x2) = 42 Reorder the terms: 6 + 1x + 5x + x2 + x2 = 42 Combine like terms: 1x + 5x = 6x 6 + 6x + x2 + x2 = 42 Combine like terms: x2 + x2 = 2x2 6 + 6x + 2x2 = 42 Solving 6 + 6x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: 6 + -42 + 6x + 2x2 = 42 + -42 Combine like terms: 6 + -42 = -36 -36 + 6x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -36 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 3x + x2) = 0 Factor a trinomial. 2((-6 + -1x)(3 + -1x)) = 0 Ignore the factor 2. Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6 Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3 So x = {-6, 3}