15a^2-43a+13=5

Solution for 15a^2-43a+13=5 equation:

Simplifying
15a2 + -43a + 13 = 5

Reorder the terms:
13 + -43a + 15a2 = 5

Solving
13 + -43a + 15a2 = 5

Solving for variable 'a'.

Reorder the terms:
13 + -5 + -43a + 15a2 = 5 + -5

Combine like terms: 13 + -5 = 8
8 + -43a + 15a2 = 5 + -5

Combine like terms: 5 + -5 = 0
8 + -43a + 15a2 = 0

Factor a trinomial.
(1 + -5a)(8 + -3a) = 0

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

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
Subproblem 2
Set the factor '(8 + -3a)' equal to zero and attempt to solve:

Simplifying
8 + -3a = 0

Solving
8 + -3a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a = 0 + -8
-3a = 0 + -8

Combine like terms: 0 + -8 = -8
-3a = -8

Divide each side by '-3'.
a = 2.666666667

Simplifying
a = 2.666666667
Solution
a = {0.2, 2.666666667}