3(a-4)=6a(3a-12)

Solution for 3(a-4)=6a(3a-12) equation:

Simplifying
3(a + -4) = 6a(3a + -12)

Reorder the terms:
3(-4 + a) = 6a(3a + -12)
(-4 * 3 + a * 3) = 6a(3a + -12)
(-12 + 3a) = 6a(3a + -12)

Reorder the terms:
-12 + 3a = 6a(-12 + 3a)
-12 + 3a = (-12 * 6a + 3a * 6a)
-12 + 3a = (-72a + 18a2)

Solving
-12 + 3a = -72a + 18a2

Solving for variable 'a'.

Combine like terms: 3a + 72a = 75a
-12 + 75a + -18a2 = -72a + 18a2 + 72a + -18a2

Reorder the terms:
-12 + 75a + -18a2 = -72a + 72a + 18a2 + -18a2

Combine like terms: -72a + 72a = 0
-12 + 75a + -18a2 = 0 + 18a2 + -18a2
-12 + 75a + -18a2 = 18a2 + -18a2

Combine like terms: 18a2 + -18a2 = 0
-12 + 75a + -18a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 25a + -6a2) = 0

Factor a trinomial.
3((-4 + a)(1 + -6a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + a)' equal to zero and attempt to solve:

Simplifying
-4 + a = 0

Solving
-4 + a = 0

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

Add '4' to each side of the equation.
-4 + 4 + a = 0 + 4

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

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

Simplifying
a = 4
Subproblem 2
Set the factor '(1 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

Solving
1 + -6a = 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 + -6a = 0 + -1

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

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

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Solution
a = {4, 0.1666666667}