(x-1)(x+2)=(x+3)(x+4)

Solution for (x-1)(x+2)=(x+3)(x+4) equation:

Simplifying
(x + -1)(x + 2) = (x + 3)(x + 4)

Reorder the terms:
(-1 + x)(x + 2) = (x + 3)(x + 4)

Reorder the terms:
(-1 + x)(2 + x) = (x + 3)(x + 4)

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = (x + 3)(x + 4)
((2 * -1 + x * -1) + x(2 + x)) = (x + 3)(x + 4)
((-2 + -1x) + x(2 + x)) = (x + 3)(x + 4)
(-2 + -1x + (2 * x + x * x)) = (x + 3)(x + 4)
(-2 + -1x + (2x + x2)) = (x + 3)(x + 4)

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

Reorder the terms:
-2 + 1x + x2 = (3 + x)(x + 4)

Reorder the terms:
-2 + 1x + x2 = (3 + x)(4 + x)

Multiply (3 + x) * (4 + x)
-2 + 1x + x2 = (3(4 + x) + x(4 + x))
-2 + 1x + x2 = ((4 * 3 + x * 3) + x(4 + x))
-2 + 1x + x2 = ((12 + 3x) + x(4 + x))
-2 + 1x + x2 = (12 + 3x + (4 * x + x * x))
-2 + 1x + x2 = (12 + 3x + (4x + x2))

Combine like terms: 3x + 4x = 7x
-2 + 1x + x2 = (12 + 7x + x2)

Add '-1x2' to each side of the equation.
-2 + 1x + x2 + -1x2 = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 0 = 12 + 7x + x2 + -1x2
-2 + 1x = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x = 12 + 7x + 0
-2 + 1x = 12 + 7x

Solving
-2 + 1x = 12 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
-2 + 1x + -7x = 12 + 7x + -7x

Combine like terms: 1x + -7x = -6x
-2 + -6x = 12 + 7x + -7x

Combine like terms: 7x + -7x = 0
-2 + -6x = 12 + 0
-2 + -6x = 12

Add '2' to each side of the equation.
-2 + 2 + -6x = 12 + 2

Combine like terms: -2 + 2 = 0
0 + -6x = 12 + 2
-6x = 12 + 2

Combine like terms: 12 + 2 = 14
-6x = 14

Divide each side by '-6'.
x = -2.333333333

Simplifying
x = -2.333333333