(x+3)(x+7)=(x+5)(x+1)

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Solution for (x+3)(x+7)=(x+5)(x+1) equation: 


Simplifying
(x + 3)(x + 7) = (x + 5)(x + 1)

Reorder the terms:
(3 + x)(x + 7) = (x + 5)(x + 1)

Reorder the terms:
(3 + x)(7 + x) = (x + 5)(x + 1)

Multiply (3 + x) * (7 + x)
(3(7 + x) + x(7 + x)) = (x + 5)(x + 1)
((7 * 3 + x * 3) + x(7 + x)) = (x + 5)(x + 1)
((21 + 3x) + x(7 + x)) = (x + 5)(x + 1)
(21 + 3x + (7 * x + x * x)) = (x + 5)(x + 1)
(21 + 3x + (7x + x2)) = (x + 5)(x + 1)

Combine like terms: 3x + 7x = 10x
(21 + 10x + x2) = (x + 5)(x + 1)

Reorder the terms:
21 + 10x + x2 = (5 + x)(x + 1)

Reorder the terms:
21 + 10x + x2 = (5 + x)(1 + x)

Multiply (5 + x) * (1 + x)
21 + 10x + x2 = (5(1 + x) + x(1 + x))
21 + 10x + x2 = ((1 * 5 + x * 5) + x(1 + x))
21 + 10x + x2 = ((5 + 5x) + x(1 + x))
21 + 10x + x2 = (5 + 5x + (1 * x + x * x))
21 + 10x + x2 = (5 + 5x + (1x + x2))

Combine like terms: 5x + 1x = 6x
21 + 10x + x2 = (5 + 6x + x2)

Add '-1x2' to each side of the equation.
21 + 10x + x2 + -1x2 = 5 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 10x + 0 = 5 + 6x + x2 + -1x2
21 + 10x = 5 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 10x = 5 + 6x + 0
21 + 10x = 5 + 6x

Solving
21 + 10x = 5 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
21 + 10x + -6x = 5 + 6x + -6x

Combine like terms: 10x + -6x = 4x
21 + 4x = 5 + 6x + -6x

Combine like terms: 6x + -6x = 0
21 + 4x = 5 + 0
21 + 4x = 5

Add '-21' to each side of the equation.
21 + -21 + 4x = 5 + -21

Combine like terms: 21 + -21 = 0
0 + 4x = 5 + -21
4x = 5 + -21

Combine like terms: 5 + -21 = -16
4x = -16

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

Simplifying
x = -4

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