6a^2-54=(a+3)(a-3)

Solution for 6a^2-54=(a+3)(a-3) equation:

Simplifying
6a2 + -54 = (a + 3)(a + -3)

Reorder the terms:
-54 + 6a2 = (a + 3)(a + -3)

Reorder the terms:
-54 + 6a2 = (3 + a)(a + -3)

Reorder the terms:
-54 + 6a2 = (3 + a)(-3 + a)

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

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

Solving
-54 + 6a2 = -9 + a2

Solving for variable 'a'.

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

Add '-1a2' to each side of the equation.
-54 + 6a2 + -1a2 = -9 + a2 + -1a2

Combine like terms: 6a2 + -1a2 = 5a2
-54 + 5a2 = -9 + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-54 + 5a2 = -9 + 0
-54 + 5a2 = -9

Add '54' to each side of the equation.
-54 + 54 + 5a2 = -9 + 54

Combine like terms: -54 + 54 = 0
0 + 5a2 = -9 + 54
5a2 = -9 + 54

Combine like terms: -9 + 54 = 45
5a2 = 45

Divide each side by '5'.
a2 = 9

Simplifying
a2 = 9

Take the square root of each side:
a = {-3, 3}