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

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


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

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

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

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

Combine like terms: 1x + 2x = 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 = 9x
2 + 3x + x2 = (20 + 9x + x2)

Add '-1x2' to each side of the equation.
2 + 3x + x2 + -1x2 = 20 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + 0 = 20 + 9x + x2 + -1x2
2 + 3x = 20 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x = 20 + 9x + 0
2 + 3x = 20 + 9x

Solving
2 + 3x = 20 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
2 + 3x + -9x = 20 + 9x + -9x

Combine like terms: 3x + -9x = -6x
2 + -6x = 20 + 9x + -9x

Combine like terms: 9x + -9x = 0
2 + -6x = 20 + 0
2 + -6x = 20

Add '-2' to each side of the equation.
2 + -2 + -6x = 20 + -2

Combine like terms: 2 + -2 = 0
0 + -6x = 20 + -2
-6x = 20 + -2

Combine like terms: 20 + -2 = 18
-6x = 18

Divide each side by '-6'.
x = -3

Simplifying
x = -3

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