16a^2=4-12a

Solution for 16a^2=4-12a equation:

Simplifying
16a2 = 4 + -12a

Solving
16a2 = 4 + -12a

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 3a + 4a2) = 0

Factor a trinomial.
4((-1 + -1a)(1 + -4a)) = 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 '(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
Solution
a = {-1, 0.25}