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

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


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

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

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

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

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

Reorder the terms:
12 + 7x + x2 = (2 + x)(x + 1)

Reorder the terms:
12 + 7x + x2 = (2 + x)(1 + x)

Multiply (2 + x) * (1 + x)
12 + 7x + x2 = (2(1 + x) + x(1 + x))
12 + 7x + x2 = ((1 * 2 + x * 2) + x(1 + x))
12 + 7x + x2 = ((2 + 2x) + x(1 + x))
12 + 7x + x2 = (2 + 2x + (1 * x + x * x))
12 + 7x + x2 = (2 + 2x + (1x + x2))

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

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

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

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

Solving
12 + 7x = 2 + 3x

Solving for variable 'x'.

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

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

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

Combine like terms: 3x + -3x = 0
12 + 4x = 2 + 0
12 + 4x = 2

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

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

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

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

Simplifying
x = -2.5

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