-50+x^2+(x+6)(x+6)=0

Solution for -50+x^2+(x+6)(x+6)=0 equation:

Simplifying
-50 + x2 + (x + 6)(x + 6) = 0

Reorder the terms:
-50 + x2 + (6 + x)(x + 6) = 0

Reorder the terms:
-50 + x2 + (6 + x)(6 + x) = 0

Multiply (6 + x) * (6 + x)
-50 + x2 + (6(6 + x) + x(6 + x)) = 0
-50 + x2 + ((6 * 6 + x * 6) + x(6 + x)) = 0
-50 + x2 + ((36 + 6x) + x(6 + x)) = 0
-50 + x2 + (36 + 6x + (6 * x + x * x)) = 0
-50 + x2 + (36 + 6x + (6x + x2)) = 0

Combine like terms: 6x + 6x = 12x
-50 + x2 + (36 + 12x + x2) = 0

Reorder the terms:
-50 + 36 + 12x + x2 + x2 = 0

Combine like terms: -50 + 36 = -14
-14 + 12x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-14 + 12x + 2x2 = 0

Solving
-14 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-7, 1}