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

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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 = 3x
(2 + 3x + x2) = (x + 3)(x + 4)

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

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

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

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

Add '-1x2' to each side of the equation.
2 + 3x + x2 + -1x2 = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + 0 = 12 + 7x + x2 + -1x2
2 + 3x = 12 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x = 12 + 7x + 0
2 + 3x = 12 + 7x

Solving
2 + 3x = 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 + 3x + -7x = 12 + 7x + -7x

Combine like terms: 3x + -7x = -4x
2 + -4x = 12 + 7x + -7x

Combine like terms: 7x + -7x = 0
2 + -4x = 12 + 0
2 + -4x = 12

Add '-2' to each side of the equation.
2 + -2 + -4x = 12 + -2

Combine like terms: 2 + -2 = 0
0 + -4x = 12 + -2
-4x = 12 + -2

Combine like terms: 12 + -2 = 10
-4x = 10

Divide each side by '-4'.
x = -2.5

Simplifying
x = -2.5

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