130*130=(n+6)*((n+6)-12)

Solution for 130*130=(n+6)*((n+6)-12) equation:

Simplifying
130 * 130 = (n + 6)((n + 6) + -12)

Multiply 130 * 130
16900 = (n + 6)((n + 6) + -12)

Reorder the terms:
16900 = (6 + n)((n + 6) + -12)

Reorder the terms:
16900 = (6 + n)((6 + n) + -12)

Remove parenthesis around (6 + n)
16900 = (6 + n)(6 + n + -12)

Reorder the terms:
16900 = (6 + n)(6 + -12 + n)

Combine like terms: 6 + -12 = -6
16900 = (6 + n)(-6 + n)

Multiply (6 + n) * (-6 + n)
16900 = (6(-6 + n) + n(-6 + n))
16900 = ((-6 * 6 + n * 6) + n(-6 + n))
16900 = ((-36 + 6n) + n(-6 + n))
16900 = (-36 + 6n + (-6 * n + n * n))
16900 = (-36 + 6n + (-6n + n2))

Combine like terms: 6n + -6n = 0
16900 = (-36 + 0 + n2)
16900 = (-36 + n2)

Solving
16900 = -36 + n2

Solving for variable 'n'.

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

Add '-1n2' to each side of the equation.
16900 + -1n2 = -36 + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
16900 + -1n2 = -36 + 0
16900 + -1n2 = -36

Add '-16900' to each side of the equation.
16900 + -16900 + -1n2 = -36 + -16900

Combine like terms: 16900 + -16900 = 0
0 + -1n2 = -36 + -16900
-1n2 = -36 + -16900

Combine like terms: -36 + -16900 = -16936
-1n2 = -16936

Divide each side by '-1'.
n2 = 16936

Simplifying
n2 = 16936

Take the square root of each side:
n = {-130.13838788, 130.13838788}