18-6=4a-4a(a-3)

Solution for 18-6=4a-4a(a-3) equation:

Simplifying
18 + -6 = 4a + -4a(a + -3)

Combine like terms: 18 + -6 = 12
12 = 4a + -4a(a + -3)

Reorder the terms:
12 = 4a + -4a(-3 + a)
12 = 4a + (-3 * -4a + a * -4a)
12 = 4a + (12a + -4a2)

Combine like terms: 4a + 12a = 16a
12 = 16a + -4a2

Solving
12 = 16a + -4a2

Solving for variable 'a'.

Reorder the terms:
12 + -16a + 4a2 = 16a + -16a + -4a2 + 4a2

Combine like terms: 16a + -16a = 0
12 + -16a + 4a2 = 0 + -4a2 + 4a2
12 + -16a + 4a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
12 + -16a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -4a + a2) = 0

Factor a trinomial.
4((1 + -1a)(3 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
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 = {1, 3}