(a+3)(a-3)=6a-18

Solution for (a+3)(a-3)=6a-18 equation:

Simplifying
(a + 3)(a + -3) = 6a + -18

Reorder the terms:
(3 + a)(a + -3) = 6a + -18

Reorder the terms:
(3 + a)(-3 + a) = 6a + -18

Multiply (3 + a) * (-3 + a)
(3(-3 + a) + a(-3 + a)) = 6a + -18
((-3 * 3 + a * 3) + a(-3 + a)) = 6a + -18
((-9 + 3a) + a(-3 + a)) = 6a + -18
(-9 + 3a + (-3 * a + a * a)) = 6a + -18
(-9 + 3a + (-3a + a2)) = 6a + -18

Combine like terms: 3a + -3a = 0
(-9 + 0 + a2) = 6a + -18
(-9 + a2) = 6a + -18

Reorder the terms:
-9 + a2 = -18 + 6a

Solving
-9 + a2 = -18 + 6a

Solving for variable 'a'.

Reorder the terms:
-9 + 18 + -6a + a2 = -18 + 6a + 18 + -6a

Combine like terms: -9 + 18 = 9
9 + -6a + a2 = -18 + 6a + 18 + -6a

Reorder the terms:
9 + -6a + a2 = -18 + 18 + 6a + -6a

Combine like terms: -18 + 18 = 0
9 + -6a + a2 = 0 + 6a + -6a
9 + -6a + a2 = 6a + -6a

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

Factor a trinomial.
(3 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {3, 3}