(x+3)(x+4)=(x+7)(x+2)

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Solution for (x+3)(x+4)=(x+7)(x+2) equation: 


Simplifying
(x + 3)(x + 4) = (x + 7)(x + 2)

Reorder the terms:
(3 + x)(x + 4) = (x + 7)(x + 2)

Reorder the terms:
(3 + x)(4 + x) = (x + 7)(x + 2)

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) = (x + 7)(x + 2)
((4 * 3 + x * 3) + x(4 + x)) = (x + 7)(x + 2)
((12 + 3x) + x(4 + x)) = (x + 7)(x + 2)
(12 + 3x + (4 * x + x * x)) = (x + 7)(x + 2)
(12 + 3x + (4x + x2)) = (x + 7)(x + 2)

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

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

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

Multiply (7 + x) * (2 + x)
12 + 7x + x2 = (7(2 + x) + x(2 + x))
12 + 7x + x2 = ((2 * 7 + x * 7) + x(2 + x))
12 + 7x + x2 = ((14 + 7x) + x(2 + x))
12 + 7x + x2 = (14 + 7x + (2 * x + x * x))
12 + 7x + x2 = (14 + 7x + (2x + x2))

Combine like terms: 7x + 2x = 9x
12 + 7x + x2 = (14 + 9x + x2)

Add '-1x2' to each side of the equation.
12 + 7x + x2 + -1x2 = 14 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 7x + 0 = 14 + 9x + x2 + -1x2
12 + 7x = 14 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 7x = 14 + 9x + 0
12 + 7x = 14 + 9x

Solving
12 + 7x = 14 + 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.
12 + 7x + -9x = 14 + 9x + -9x

Combine like terms: 7x + -9x = -2x
12 + -2x = 14 + 9x + -9x

Combine like terms: 9x + -9x = 0
12 + -2x = 14 + 0
12 + -2x = 14

Add '-12' to each side of the equation.
12 + -12 + -2x = 14 + -12

Combine like terms: 12 + -12 = 0
0 + -2x = 14 + -12
-2x = 14 + -12

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

Divide each side by '-2'.
x = -1

Simplifying
x = -1

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