(x+1)(x+4)=(2-x)(x+2)

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Solution for (x+1)(x+4)=(2-x)(x+2) equation:


Simplifying
(x + 1)(x + 4) = (2 + -1x)(x + 2)

Reorder the terms:
(1 + x)(x + 4) = (2 + -1x)(x + 2)

Reorder the terms:
(1 + x)(4 + x) = (2 + -1x)(x + 2)

Multiply (1 + x) * (4 + x)
(1(4 + x) + x(4 + x)) = (2 + -1x)(x + 2)
((4 * 1 + x * 1) + x(4 + x)) = (2 + -1x)(x + 2)
((4 + 1x) + x(4 + x)) = (2 + -1x)(x + 2)
(4 + 1x + (4 * x + x * x)) = (2 + -1x)(x + 2)
(4 + 1x + (4x + x2)) = (2 + -1x)(x + 2)

Combine like terms: 1x + 4x = 5x
(4 + 5x + x2) = (2 + -1x)(x + 2)

Reorder the terms:
4 + 5x + x2 = (2 + -1x)(2 + x)

Multiply (2 + -1x) * (2 + x)
4 + 5x + x2 = (2(2 + x) + -1x * (2 + x))
4 + 5x + x2 = ((2 * 2 + x * 2) + -1x * (2 + x))
4 + 5x + x2 = ((4 + 2x) + -1x * (2 + x))
4 + 5x + x2 = (4 + 2x + (2 * -1x + x * -1x))
4 + 5x + x2 = (4 + 2x + (-2x + -1x2))

Combine like terms: 2x + -2x = 0
4 + 5x + x2 = (4 + 0 + -1x2)
4 + 5x + x2 = (4 + -1x2)

Add '-4' to each side of the equation.
4 + 5x + -4 + x2 = 4 + -4 + -1x2

Reorder the terms:
4 + -4 + 5x + x2 = 4 + -4 + -1x2

Combine like terms: 4 + -4 = 0
0 + 5x + x2 = 4 + -4 + -1x2
5x + x2 = 4 + -4 + -1x2

Combine like terms: 4 + -4 = 0
5x + x2 = 0 + -1x2
5x + x2 = -1x2

Solving
5x + x2 = -1x2

Solving for variable 'x'.

Combine like terms: x2 + x2 = 2x2
5x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
5x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 2x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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 = -2.5

Solution

x = {0, -2.5}

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