(5+x)(6-x)+(6+x)(5-x)=0

Solution for (5+x)(6-x)+(6+x)(5-x)=0 equation:

Simplifying
(5 + x)(6 + -1x) + (6 + x)(5 + -1x) = 0

Multiply (5 + x) * (6 + -1x)
(5(6 + -1x) + x(6 + -1x)) + (6 + x)(5 + -1x) = 0
((6 * 5 + -1x * 5) + x(6 + -1x)) + (6 + x)(5 + -1x) = 0
((30 + -5x) + x(6 + -1x)) + (6 + x)(5 + -1x) = 0
(30 + -5x + (6 * x + -1x * x)) + (6 + x)(5 + -1x) = 0
(30 + -5x + (6x + -1x2)) + (6 + x)(5 + -1x) = 0

Combine like terms: -5x + 6x = 1x
(30 + 1x + -1x2) + (6 + x)(5 + -1x) = 0

Multiply (6 + x) * (5 + -1x)
30 + 1x + -1x2 + (6(5 + -1x) + x(5 + -1x)) = 0
30 + 1x + -1x2 + ((5 * 6 + -1x * 6) + x(5 + -1x)) = 0
30 + 1x + -1x2 + ((30 + -6x) + x(5 + -1x)) = 0
30 + 1x + -1x2 + (30 + -6x + (5 * x + -1x * x)) = 0
30 + 1x + -1x2 + (30 + -6x + (5x + -1x2)) = 0

Combine like terms: -6x + 5x = -1x
30 + 1x + -1x2 + (30 + -1x + -1x2) = 0

Reorder the terms:
30 + 30 + 1x + -1x + -1x2 + -1x2 = 0

Combine like terms: 30 + 30 = 60
60 + 1x + -1x + -1x2 + -1x2 = 0

Combine like terms: 1x + -1x = 0
60 + 0 + -1x2 + -1x2 = 0
60 + -1x2 + -1x2 = 0

Combine like terms: -1x2 + -1x2 = -2x2
60 + -2x2 = 0

Solving
60 + -2x2 = 0

Solving for variable 'x'.

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

Add '-60' to each side of the equation.
60 + -60 + -2x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -2x2 = 0 + -60
-2x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-2x2 = -60

Divide each side by '-2'.
x2 = 30

Simplifying
x2 = 30

Take the square root of each side:
x = {-5.477225575, 5.477225575}