(x+5)(5-x)=(12+x)(4-x)+1

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Solution for (x+5)(5-x)=(12+x)(4-x)+1 equation: 


Simplifying
(x + 5)(5 + -1x) = (12 + x)(4 + -1x) + 1

Reorder the terms:
(5 + x)(5 + -1x) = (12 + x)(4 + -1x) + 1

Multiply (5 + x) * (5 + -1x)
(5(5 + -1x) + x(5 + -1x)) = (12 + x)(4 + -1x) + 1
((5 * 5 + -1x * 5) + x(5 + -1x)) = (12 + x)(4 + -1x) + 1
((25 + -5x) + x(5 + -1x)) = (12 + x)(4 + -1x) + 1
(25 + -5x + (5 * x + -1x * x)) = (12 + x)(4 + -1x) + 1
(25 + -5x + (5x + -1x2)) = (12 + x)(4 + -1x) + 1

Combine like terms: -5x + 5x = 0
(25 + 0 + -1x2) = (12 + x)(4 + -1x) + 1
(25 + -1x2) = (12 + x)(4 + -1x) + 1

Multiply (12 + x) * (4 + -1x)
25 + -1x2 = (12(4 + -1x) + x(4 + -1x)) + 1
25 + -1x2 = ((4 * 12 + -1x * 12) + x(4 + -1x)) + 1
25 + -1x2 = ((48 + -12x) + x(4 + -1x)) + 1
25 + -1x2 = (48 + -12x + (4 * x + -1x * x)) + 1
25 + -1x2 = (48 + -12x + (4x + -1x2)) + 1

Combine like terms: -12x + 4x = -8x
25 + -1x2 = (48 + -8x + -1x2) + 1

Reorder the terms:
25 + -1x2 = 48 + 1 + -8x + -1x2

Combine like terms: 48 + 1 = 49
25 + -1x2 = 49 + -8x + -1x2

Add 'x2' to each side of the equation.
25 + -1x2 + x2 = 49 + -8x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
25 + 0 = 49 + -8x + -1x2 + x2
25 = 49 + -8x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
25 = 49 + -8x + 0
25 = 49 + -8x

Solving
25 = 49 + -8x

Solving for variable 'x'.

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

Add '8x' to each side of the equation.
25 + 8x = 49 + -8x + 8x

Combine like terms: -8x + 8x = 0
25 + 8x = 49 + 0
25 + 8x = 49

Add '-25' to each side of the equation.
25 + -25 + 8x = 49 + -25

Combine like terms: 25 + -25 = 0
0 + 8x = 49 + -25
8x = 49 + -25

Combine like terms: 49 + -25 = 24
8x = 24

Divide each side by '8'.
x = 3

Simplifying
x = 3

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