(x+3)(x+4)-(x+5)(x+1)=0

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Solution for (x+3)(x+4)-(x+5)(x+1)=0 equation: 


Simplifying
(x + 3)(x + 4) + -1(x + 5)(x + 1) = 0

Reorder the terms:
(3 + x)(x + 4) + -1(x + 5)(x + 1) = 0

Reorder the terms:
(3 + x)(4 + x) + -1(x + 5)(x + 1) = 0

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) + -1(x + 5)(x + 1) = 0
((4 * 3 + x * 3) + x(4 + x)) + -1(x + 5)(x + 1) = 0
((12 + 3x) + x(4 + x)) + -1(x + 5)(x + 1) = 0
(12 + 3x + (4 * x + x * x)) + -1(x + 5)(x + 1) = 0
(12 + 3x + (4x + x2)) + -1(x + 5)(x + 1) = 0

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) + -1(x + 5)(x + 1) = 0

Reorder the terms:
12 + 7x + x2 + -1(5 + x)(x + 1) = 0

Reorder the terms:
12 + 7x + x2 + -1(5 + x)(1 + x) = 0

Multiply (5 + x) * (1 + x)
12 + 7x + x2 + -1(5(1 + x) + x(1 + x)) = 0
12 + 7x + x2 + -1((1 * 5 + x * 5) + x(1 + x)) = 0
12 + 7x + x2 + -1((5 + 5x) + x(1 + x)) = 0
12 + 7x + x2 + -1(5 + 5x + (1 * x + x * x)) = 0
12 + 7x + x2 + -1(5 + 5x + (1x + x2)) = 0

Combine like terms: 5x + 1x = 6x
12 + 7x + x2 + -1(5 + 6x + x2) = 0
12 + 7x + x2 + (5 * -1 + 6x * -1 + x2 * -1) = 0
12 + 7x + x2 + (-5 + -6x + -1x2) = 0

Reorder the terms:
12 + -5 + 7x + -6x + x2 + -1x2 = 0

Combine like terms: 12 + -5 = 7
7 + 7x + -6x + x2 + -1x2 = 0

Combine like terms: 7x + -6x = 1x
7 + 1x + x2 + -1x2 = 0

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

Solving
7 + 1x = 0

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + 1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 1x = 0 + -7
1x = 0 + -7

Combine like terms: 0 + -7 = -7
1x = -7

Divide each side by '1'.
x = -7

Simplifying
x = -7

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