(20+x)*(20-x)=(x+2)*(46-x)

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Solution for (20+x)*(20-x)=(x+2)*(46-x) equation: 


Simplifying
(20 + x)(20 + -1x) = (x + 2)(46 + -1x)

Multiply (20 + x) * (20 + -1x)
(20(20 + -1x) + x(20 + -1x)) = (x + 2)(46 + -1x)
((20 * 20 + -1x * 20) + x(20 + -1x)) = (x + 2)(46 + -1x)
((400 + -20x) + x(20 + -1x)) = (x + 2)(46 + -1x)
(400 + -20x + (20 * x + -1x * x)) = (x + 2)(46 + -1x)
(400 + -20x + (20x + -1x2)) = (x + 2)(46 + -1x)

Combine like terms: -20x + 20x = 0
(400 + 0 + -1x2) = (x + 2)(46 + -1x)
(400 + -1x2) = (x + 2)(46 + -1x)

Reorder the terms:
400 + -1x2 = (2 + x)(46 + -1x)

Multiply (2 + x) * (46 + -1x)
400 + -1x2 = (2(46 + -1x) + x(46 + -1x))
400 + -1x2 = ((46 * 2 + -1x * 2) + x(46 + -1x))
400 + -1x2 = ((92 + -2x) + x(46 + -1x))
400 + -1x2 = (92 + -2x + (46 * x + -1x * x))
400 + -1x2 = (92 + -2x + (46x + -1x2))

Combine like terms: -2x + 46x = 44x
400 + -1x2 = (92 + 44x + -1x2)

Add 'x2' to each side of the equation.
400 + -1x2 + x2 = 92 + 44x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
400 + 0 = 92 + 44x + -1x2 + x2
400 = 92 + 44x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
400 = 92 + 44x + 0
400 = 92 + 44x

Solving
400 = 92 + 44x

Solving for variable 'x'.

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

Add '-44x' to each side of the equation.
400 + -44x = 92 + 44x + -44x

Combine like terms: 44x + -44x = 0
400 + -44x = 92 + 0
400 + -44x = 92

Add '-400' to each side of the equation.
400 + -400 + -44x = 92 + -400

Combine like terms: 400 + -400 = 0
0 + -44x = 92 + -400
-44x = 92 + -400

Combine like terms: 92 + -400 = -308
-44x = -308

Divide each side by '-44'.
x = 7

Simplifying
x = 7

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