(6+x)(6+x)=146-x*x

Solution for (6+x)(6+x)=146-x*x equation:

Simplifying
(6 + x)(6 + x) = 146 + -1x * x

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) = 146 + -1x * x
((6 * 6 + x * 6) + x(6 + x)) = 146 + -1x * x
((36 + 6x) + x(6 + x)) = 146 + -1x * x
(36 + 6x + (6 * x + x * x)) = 146 + -1x * x
(36 + 6x + (6x + x2)) = 146 + -1x * x

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) = 146 + -1x * x

Multiply x * x
36 + 12x + x2 = 146 + -1x2

Solving
36 + 12x + x2 = 146 + -1x2

Solving for variable 'x'.

Reorder the terms:
36 + -146 + 12x + x2 + x2 = 146 + -1x2 + -146 + x2

Combine like terms: 36 + -146 = -110
-110 + 12x + x2 + x2 = 146 + -1x2 + -146 + x2

Combine like terms: x2 + x2 = 2x2
-110 + 12x + 2x2 = 146 + -1x2 + -146 + x2

Reorder the terms:
-110 + 12x + 2x2 = 146 + -146 + -1x2 + x2

Combine like terms: 146 + -146 = 0
-110 + 12x + 2x2 = 0 + -1x2 + x2
-110 + 12x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-110 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 6x + x2) = 0

Factor a trinomial.
2((-11 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-11, 5}