5a^2=16a-12

Solution for 5a^2=16a-12 equation:

Simplifying
5a2 = 16a + -12

Reorder the terms:
5a2 = -12 + 16a

Solving
5a2 = -12 + 16a

Solving for variable 'a'.

Reorder the terms:
12 + -16a + 5a2 = -12 + 16a + 12 + -16a

Reorder the terms:
12 + -16a + 5a2 = -12 + 12 + 16a + -16a

Combine like terms: -12 + 12 = 0
12 + -16a + 5a2 = 0 + 16a + -16a
12 + -16a + 5a2 = 16a + -16a

Combine like terms: 16a + -16a = 0
12 + -16a + 5a2 = 0

Factor a trinomial.
(6 + -5a)(2 + -1a) = 0

Subproblem 1
Set the factor '(6 + -5a)' equal to zero and attempt to solve:

Simplifying
6 + -5a = 0

Solving
6 + -5a = 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 + -5a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5a = 0 + -6
-5a = 0 + -6

Combine like terms: 0 + -6 = -6
-5a = -6

Divide each side by '-5'.
a = 1.2

Simplifying
a = 1.2
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {1.2, 2}