(x+5)(x+3)=(x+1)(x+7)+10

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Solution for (x+5)(x+3)=(x+1)(x+7)+10 equation: 


Simplifying
(x + 5)(x + 3) = (x + 1)(x + 7) + 10

Reorder the terms:
(5 + x)(x + 3) = (x + 1)(x + 7) + 10

Reorder the terms:
(5 + x)(3 + x) = (x + 1)(x + 7) + 10

Multiply (5 + x) * (3 + x)
(5(3 + x) + x(3 + x)) = (x + 1)(x + 7) + 10
((3 * 5 + x * 5) + x(3 + x)) = (x + 1)(x + 7) + 10
((15 + 5x) + x(3 + x)) = (x + 1)(x + 7) + 10
(15 + 5x + (3 * x + x * x)) = (x + 1)(x + 7) + 10
(15 + 5x + (3x + x2)) = (x + 1)(x + 7) + 10

Combine like terms: 5x + 3x = 8x
(15 + 8x + x2) = (x + 1)(x + 7) + 10

Reorder the terms:
15 + 8x + x2 = (1 + x)(x + 7) + 10

Reorder the terms:
15 + 8x + x2 = (1 + x)(7 + x) + 10

Multiply (1 + x) * (7 + x)
15 + 8x + x2 = (1(7 + x) + x(7 + x)) + 10
15 + 8x + x2 = ((7 * 1 + x * 1) + x(7 + x)) + 10
15 + 8x + x2 = ((7 + 1x) + x(7 + x)) + 10
15 + 8x + x2 = (7 + 1x + (7 * x + x * x)) + 10
15 + 8x + x2 = (7 + 1x + (7x + x2)) + 10

Combine like terms: 1x + 7x = 8x
15 + 8x + x2 = (7 + 8x + x2) + 10

Reorder the terms:
15 + 8x + x2 = 7 + 10 + 8x + x2

Combine like terms: 7 + 10 = 17
15 + 8x + x2 = 17 + 8x + x2

Add '-8x' to each side of the equation.
15 + 8x + -8x + x2 = 17 + 8x + -8x + x2

Combine like terms: 8x + -8x = 0
15 + 0 + x2 = 17 + 8x + -8x + x2
15 + x2 = 17 + 8x + -8x + x2

Combine like terms: 8x + -8x = 0
15 + x2 = 17 + 0 + x2
15 + x2 = 17 + x2

Add '-1x2' to each side of the equation.
15 + x2 + -1x2 = 17 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 0 = 17 + x2 + -1x2
15 = 17 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 = 17 + 0
15 = 17

Solving
15 = 17

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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