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Simplifying (2x + 1)(x + 4) + -1(x + 2)(x + -3) = (x + 5)(x + -1) Reorder the terms: (1 + 2x)(x + 4) + -1(x + 2)(x + -3) = (x + 5)(x + -1) Reorder the terms: (1 + 2x)(4 + x) + -1(x + 2)(x + -3) = (x + 5)(x + -1) Multiply (1 + 2x) * (4 + x) (1(4 + x) + 2x * (4 + x)) + -1(x + 2)(x + -3) = (x + 5)(x + -1) ((4 * 1 + x * 1) + 2x * (4 + x)) + -1(x + 2)(x + -3) = (x + 5)(x + -1) ((4 + 1x) + 2x * (4 + x)) + -1(x + 2)(x + -3) = (x + 5)(x + -1) (4 + 1x + (4 * 2x + x * 2x)) + -1(x + 2)(x + -3) = (x + 5)(x + -1) (4 + 1x + (8x + 2x2)) + -1(x + 2)(x + -3) = (x + 5)(x + -1) Combine like terms: 1x + 8x = 9x (4 + 9x + 2x2) + -1(x + 2)(x + -3) = (x + 5)(x + -1) Reorder the terms: 4 + 9x + 2x2 + -1(2 + x)(x + -3) = (x + 5)(x + -1) Reorder the terms: 4 + 9x + 2x2 + -1(2 + x)(-3 + x) = (x + 5)(x + -1) Multiply (2 + x) * (-3 + x) 4 + 9x + 2x2 + -1(2(-3 + x) + x(-3 + x)) = (x + 5)(x + -1) 4 + 9x + 2x2 + -1((-3 * 2 + x * 2) + x(-3 + x)) = (x + 5)(x + -1) 4 + 9x + 2x2 + -1((-6 + 2x) + x(-3 + x)) = (x + 5)(x + -1) 4 + 9x + 2x2 + -1(-6 + 2x + (-3 * x + x * x)) = (x + 5)(x + -1) 4 + 9x + 2x2 + -1(-6 + 2x + (-3x + x2)) = (x + 5)(x + -1) Combine like terms: 2x + -3x = -1x 4 + 9x + 2x2 + -1(-6 + -1x + x2) = (x + 5)(x + -1) 4 + 9x + 2x2 + (-6 * -1 + -1x * -1 + x2 * -1) = (x + 5)(x + -1) 4 + 9x + 2x2 + (6 + 1x + -1x2) = (x + 5)(x + -1) Reorder the terms: 4 + 6 + 9x + 1x + 2x2 + -1x2 = (x + 5)(x + -1) Combine like terms: 4 + 6 = 10 10 + 9x + 1x + 2x2 + -1x2 = (x + 5)(x + -1) Combine like terms: 9x + 1x = 10x 10 + 10x + 2x2 + -1x2 = (x + 5)(x + -1) Combine like terms: 2x2 + -1x2 = 1x2 10 + 10x + 1x2 = (x + 5)(x + -1) Reorder the terms: 10 + 10x + 1x2 = (5 + x)(x + -1) Reorder the terms: 10 + 10x + 1x2 = (5 + x)(-1 + x) Multiply (5 + x) * (-1 + x) 10 + 10x + 1x2 = (5(-1 + x) + x(-1 + x)) 10 + 10x + 1x2 = ((-1 * 5 + x * 5) + x(-1 + x)) 10 + 10x + 1x2 = ((-5 + 5x) + x(-1 + x)) 10 + 10x + 1x2 = (-5 + 5x + (-1 * x + x * x)) 10 + 10x + 1x2 = (-5 + 5x + (-1x + x2)) Combine like terms: 5x + -1x = 4x 10 + 10x + 1x2 = (-5 + 4x + x2) Solving 10 + 10x + 1x2 = -5 + 4x + x2 Solving for variable 'x'. Reorder the terms: 10 + 5 + 10x + -4x + 1x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2 Combine like terms: 10 + 5 = 15 15 + 10x + -4x + 1x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2 Combine like terms: 10x + -4x = 6x 15 + 6x + 1x2 + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2 Combine like terms: 1x2 + -1x2 = 0 15 + 6x + 0 = -5 + 4x + x2 + 5 + -4x + -1x2 15 + 6x = -5 + 4x + x2 + 5 + -4x + -1x2 Reorder the terms: 15 + 6x = -5 + 5 + 4x + -4x + x2 + -1x2 Combine like terms: -5 + 5 = 0 15 + 6x = 0 + 4x + -4x + x2 + -1x2 15 + 6x = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 15 + 6x = 0 + x2 + -1x2 15 + 6x = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + 6x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 2x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {-2.5}
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