=(3ab+c)(c-3ab)

Solution for =(3ab+c)(c-3ab) equation:

Simplifying
0 = (3ab + c)(c + -3ab)

Reorder the terms:
0 = (3ab + c)(-3ab + c)

Multiply (3ab + c) * (-3ab + c)
0 = (3ab * (-3ab + c) + c(-3ab + c))
0 = ((-3ab * 3ab + c * 3ab) + c(-3ab + c))

Reorder the terms:
0 = ((3abc + -9a2b2) + c(-3ab + c))
0 = ((3abc + -9a2b2) + c(-3ab + c))
0 = (3abc + -9a2b2 + (-3ab * c + c * c))
0 = (3abc + -9a2b2 + (-3abc + c2))

Reorder the terms:
0 = (3abc + -3abc + -9a2b2 + c2)

Combine like terms: 3abc + -3abc = 0
0 = (0 + -9a2b2 + c2)
0 = (-9a2b2 + c2)

Solving
0 = -9a2b2 + c2

Solving for variable 'a'.

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

Add '9a2b2' to each side of the equation.
0 + 9a2b2 = -9a2b2 + 9a2b2 + c2
Remove the zero:
9a2b2 = -9a2b2 + 9a2b2 + c2

Combine like terms: -9a2b2 + 9a2b2 = 0
9a2b2 = 0 + c2
9a2b2 = c2

Divide each side by '9b2'.
a2 = 0.1111111111b-2c2

Simplifying
a2 = 0.1111111111b-2c2

Take the square root of each side:
a = {-0.333333333b-1c, 0.333333333b-1c}