(47-x)*(25+x)=(9+x)*(13+x)

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Solution for (47-x)*(25+x)=(9+x)*(13+x) equation: 


Simplifying
(47 + -1x)(25 + x) = (9 + x)(13 + x)

Multiply (47 + -1x) * (25 + x)
(47(25 + x) + -1x * (25 + x)) = (9 + x)(13 + x)
((25 * 47 + x * 47) + -1x * (25 + x)) = (9 + x)(13 + x)
((1175 + 47x) + -1x * (25 + x)) = (9 + x)(13 + x)
(1175 + 47x + (25 * -1x + x * -1x)) = (9 + x)(13 + x)
(1175 + 47x + (-25x + -1x2)) = (9 + x)(13 + x)

Combine like terms: 47x + -25x = 22x
(1175 + 22x + -1x2) = (9 + x)(13 + x)

Multiply (9 + x) * (13 + x)
1175 + 22x + -1x2 = (9(13 + x) + x(13 + x))
1175 + 22x + -1x2 = ((13 * 9 + x * 9) + x(13 + x))
1175 + 22x + -1x2 = ((117 + 9x) + x(13 + x))
1175 + 22x + -1x2 = (117 + 9x + (13 * x + x * x))
1175 + 22x + -1x2 = (117 + 9x + (13x + x2))

Combine like terms: 9x + 13x = 22x
1175 + 22x + -1x2 = (117 + 22x + x2)

Add '-22x' to each side of the equation.
1175 + 22x + -22x + -1x2 = 117 + 22x + -22x + x2

Combine like terms: 22x + -22x = 0
1175 + 0 + -1x2 = 117 + 22x + -22x + x2
1175 + -1x2 = 117 + 22x + -22x + x2

Combine like terms: 22x + -22x = 0
1175 + -1x2 = 117 + 0 + x2
1175 + -1x2 = 117 + x2

Solving
1175 + -1x2 = 117 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
1175 + -1x2 + -1x2 = 117 + x2 + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
1175 + -2x2 = 117 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1175 + -2x2 = 117 + 0
1175 + -2x2 = 117

Add '-1175' to each side of the equation.
1175 + -1175 + -2x2 = 117 + -1175

Combine like terms: 1175 + -1175 = 0
0 + -2x2 = 117 + -1175
-2x2 = 117 + -1175

Combine like terms: 117 + -1175 = -1058
-2x2 = -1058

Divide each side by '-2'.
x2 = 529

Simplifying
x2 = 529

Take the square root of each side:
x = {-23, 23}

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