(x+3)(x+7)-(x+1)(x+5)=0

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Solution for (x+3)(x+7)-(x+1)(x+5)=0 equation: 


Simplifying
(x + 3)(x + 7) + -1(x + 1)(x + 5) = 0

Reorder the terms:
(3 + x)(x + 7) + -1(x + 1)(x + 5) = 0

Reorder the terms:
(3 + x)(7 + x) + -1(x + 1)(x + 5) = 0

Multiply (3 + x) * (7 + x)
(3(7 + x) + x(7 + x)) + -1(x + 1)(x + 5) = 0
((7 * 3 + x * 3) + x(7 + x)) + -1(x + 1)(x + 5) = 0
((21 + 3x) + x(7 + x)) + -1(x + 1)(x + 5) = 0
(21 + 3x + (7 * x + x * x)) + -1(x + 1)(x + 5) = 0
(21 + 3x + (7x + x2)) + -1(x + 1)(x + 5) = 0

Combine like terms: 3x + 7x = 10x
(21 + 10x + x2) + -1(x + 1)(x + 5) = 0

Reorder the terms:
21 + 10x + x2 + -1(1 + x)(x + 5) = 0

Reorder the terms:
21 + 10x + x2 + -1(1 + x)(5 + x) = 0

Multiply (1 + x) * (5 + x)
21 + 10x + x2 + -1(1(5 + x) + x(5 + x)) = 0
21 + 10x + x2 + -1((5 * 1 + x * 1) + x(5 + x)) = 0
21 + 10x + x2 + -1((5 + 1x) + x(5 + x)) = 0
21 + 10x + x2 + -1(5 + 1x + (5 * x + x * x)) = 0
21 + 10x + x2 + -1(5 + 1x + (5x + x2)) = 0

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

Reorder the terms:
21 + -5 + 10x + -6x + x2 + -1x2 = 0

Combine like terms: 21 + -5 = 16
16 + 10x + -6x + x2 + -1x2 = 0

Combine like terms: 10x + -6x = 4x
16 + 4x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
16 + 4x + 0 = 0
16 + 4x = 0

Solving
16 + 4x = 0

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + 4x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 4x = 0 + -16
4x = 0 + -16

Combine like terms: 0 + -16 = -16
4x = -16

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

Simplifying
x = -4

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