6a-54=(a+3)(a-3)

Solution for 6a-54=(a+3)(a-3) equation:

Simplifying
6a + -54 = (a + 3)(a + -3)

Reorder the terms:
-54 + 6a = (a + 3)(a + -3)

Reorder the terms:
-54 + 6a = (3 + a)(a + -3)

Reorder the terms:
-54 + 6a = (3 + a)(-3 + a)

Multiply (3 + a) * (-3 + a)
-54 + 6a = (3(-3 + a) + a(-3 + a))
-54 + 6a = ((-3 * 3 + a * 3) + a(-3 + a))
-54 + 6a = ((-9 + 3a) + a(-3 + a))
-54 + 6a = (-9 + 3a + (-3 * a + a * a))
-54 + 6a = (-9 + 3a + (-3a + a2))

Combine like terms: 3a + -3a = 0
-54 + 6a = (-9 + 0 + a2)
-54 + 6a = (-9 + a2)

Solving
-54 + 6a = -9 + a2

Solving for variable 'a'.

Reorder the terms:
-54 + 9 + 6a + -1a2 = -9 + a2 + 9 + -1a2

Combine like terms: -54 + 9 = -45
-45 + 6a + -1a2 = -9 + a2 + 9 + -1a2

Reorder the terms:
-45 + 6a + -1a2 = -9 + 9 + a2 + -1a2

Combine like terms: -9 + 9 = 0
-45 + 6a + -1a2 = 0 + a2 + -1a2
-45 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-45 + 6a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
45 + -6a + a2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -6a + -45 + a2 = 0 + -45

Reorder the terms:
45 + -45 + -6a + a2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -6a + a2 = 0 + -45
-6a + a2 = 0 + -45

Combine like terms: 0 + -45 = -45
-6a + a2 = -45

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -45 + 9

Reorder the terms:
9 + -6a + a2 = -45 + 9

Combine like terms: -45 + 9 = -36
9 + -6a + a2 = -36

Factor a perfect square on the left side:
(a + -3)(a + -3) = -36

Can't calculate square root of the right side.

The solution to this equation could not be determined.