5a^2-17=12a

Solution for 5a^2-17=12a equation:

Simplifying
5a2 + -17 = 12a

Reorder the terms:
-17 + 5a2 = 12a

Solving
-17 + 5a2 = 12a

Solving for variable 'a'.

Reorder the terms:
-17 + -12a + 5a2 = 12a + -12a

Combine like terms: 12a + -12a = 0
-17 + -12a + 5a2 = 0

Factor a trinomial.
(-1 + -1a)(17 + -5a) = 0

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 '(17 + -5a)' equal to zero and attempt to solve:

Simplifying
17 + -5a = 0

Solving
17 + -5a = 0

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

Add '-17' to each side of the equation.
17 + -17 + -5a = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -5a = 0 + -17
-5a = 0 + -17

Combine like terms: 0 + -17 = -17
-5a = -17

Divide each side by '-5'.
a = 3.4

Simplifying
a = 3.4
Solution
a = {-1, 3.4}