(10y+x)(10y-x)=

Solution for (10y+x)(10y-x)= equation:

Simplifying
(10y + x)(10y + -1x) = 0

Reorder the terms:
(x + 10y)(10y + -1x) = 0

Reorder the terms:
(x + 10y)(-1x + 10y) = 0

Multiply (x + 10y) * (-1x + 10y)
(x(-1x + 10y) + 10y * (-1x + 10y)) = 0
((-1x * x + 10y * x) + 10y * (-1x + 10y)) = 0

Reorder the terms:
((10xy + -1x2) + 10y * (-1x + 10y)) = 0
((10xy + -1x2) + 10y * (-1x + 10y)) = 0
(10xy + -1x2 + (-1x * 10y + 10y * 10y)) = 0
(10xy + -1x2 + (-10xy + 100y2)) = 0

Reorder the terms:
(10xy + -10xy + -1x2 + 100y2) = 0

Combine like terms: 10xy + -10xy = 0
(0 + -1x2 + 100y2) = 0
(-1x2 + 100y2) = 0

Solving
-1x2 + 100y2 = 0

Solving for variable 'x'.

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

Add '-100y2' to each side of the equation.
-1x2 + 100y2 + -100y2 = 0 + -100y2

Combine like terms: 100y2 + -100y2 = 0
-1x2 + 0 = 0 + -100y2
-1x2 = 0 + -100y2
Remove the zero:
-1x2 = -100y2

Divide each side by '-1'.
x2 = 100y2

Simplifying
x2 = 100y2

Take the square root of each side:
x = {-10y, 10y}