2a^2-4a+17a-45=0

Solution for 2a^2-4a+17a-45=0 equation:

Simplifying
2a2 + -4a + 17a + -45 = 0

Reorder the terms:
-45 + -4a + 17a + 2a2 = 0

Combine like terms: -4a + 17a = 13a
-45 + 13a + 2a2 = 0

Solving
-45 + 13a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(5 + -2a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-9, 2.5}