(x+2)(x+1)=(x+4)(x-5)

Solution for (x+2)(x+1)=(x+4)(x-5) equation:

Simplifying
(x + 2)(x + 1) = (x + 4)(x + -5)

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

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

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

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = (x + 4)(x + -5)

Reorder the terms:
2 + 3x + x2 = (4 + x)(x + -5)

Reorder the terms:
2 + 3x + x2 = (4 + x)(-5 + x)

Multiply (4 + x) * (-5 + x)
2 + 3x + x2 = (4(-5 + x) + x(-5 + x))
2 + 3x + x2 = ((-5 * 4 + x * 4) + x(-5 + x))
2 + 3x + x2 = ((-20 + 4x) + x(-5 + x))
2 + 3x + x2 = (-20 + 4x + (-5 * x + x * x))
2 + 3x + x2 = (-20 + 4x + (-5x + x2))

Combine like terms: 4x + -5x = -1x
2 + 3x + x2 = (-20 + -1x + x2)

Add '-1x2' to each side of the equation.
2 + 3x + x2 + -1x2 = -20 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + 0 = -20 + -1x + x2 + -1x2
2 + 3x = -20 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x = -20 + -1x + 0
2 + 3x = -20 + -1x

Solving
2 + 3x = -20 + -1x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'x' to each side of the equation.
2 + 3x + x = -20 + -1x + x

Combine like terms: 3x + x = 4x
2 + 4x = -20 + -1x + x

Combine like terms: -1x + x = 0
2 + 4x = -20 + 0
2 + 4x = -20

Add '-2' to each side of the equation.
2 + -2 + 4x = -20 + -2

Combine like terms: 2 + -2 = 0
0 + 4x = -20 + -2
4x = -20 + -2

Combine like terms: -20 + -2 = -22
4x = -22

Divide each side by '4'.
x = -5.5

Simplifying
x = -5.5