2(a-6)=4a(-2a+12)

Solution for 2(a-6)=4a(-2a+12) equation:

Simplifying
2(a + -6) = 4a(-2a + 12)

Reorder the terms:
2(-6 + a) = 4a(-2a + 12)
(-6 * 2 + a * 2) = 4a(-2a + 12)
(-12 + 2a) = 4a(-2a + 12)

Reorder the terms:
-12 + 2a = 4a(12 + -2a)
-12 + 2a = (12 * 4a + -2a * 4a)
-12 + 2a = (48a + -8a2)

Solving
-12 + 2a = 48a + -8a2

Solving for variable 'a'.

Combine like terms: 2a + -48a = -46a
-12 + -46a + 8a2 = 48a + -8a2 + -48a + 8a2

Reorder the terms:
-12 + -46a + 8a2 = 48a + -48a + -8a2 + 8a2

Combine like terms: 48a + -48a = 0
-12 + -46a + 8a2 = 0 + -8a2 + 8a2
-12 + -46a + 8a2 = -8a2 + 8a2

Combine like terms: -8a2 + 8a2 = 0
-12 + -46a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -23a + 4a2) = 0

Factor a trinomial.
2((-1 + -4a)(6 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4a)' equal to zero and attempt to solve:

Simplifying
-1 + -4a = 0

Solving
-1 + -4a = 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 + -4a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4a = 0 + 1
-4a = 0 + 1

Combine like terms: 0 + 1 = 1
-4a = 1

Divide each side by '-4'.
a = -0.25

Simplifying
a = -0.25
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

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

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

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-0.25, 6}