(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 = 6x
15 + 8x + x2 = (-7 + 6x + x2) + 10

Reorder the terms:
15 + 8x + x2 = -7 + 10 + 6x + x2

Combine like terms: -7 + 10 = 3
15 + 8x + x2 = 3 + 6x + x2

Add '-1x2' to each side of the equation.
15 + 8x + x2 + -1x2 = 3 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 0 = 3 + 6x + x2 + -1x2
15 + 8x = 3 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x = 3 + 6x + 0
15 + 8x = 3 + 6x

Solving
15 + 8x = 3 + 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.
15 + 8x + -6x = 3 + 6x + -6x

Combine like terms: 8x + -6x = 2x
15 + 2x = 3 + 6x + -6x

Combine like terms: 6x + -6x = 0
15 + 2x = 3 + 0
15 + 2x = 3

Add '-15' to each side of the equation.
15 + -15 + 2x = 3 + -15

Combine like terms: 15 + -15 = 0
0 + 2x = 3 + -15
2x = 3 + -15

Combine like terms: 3 + -15 = -12
2x = -12

Divide each side by '2'.
x = -6

Simplifying
x = -6

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