2a^2-17a=-30

Solution for 2a^2-17a=-30 equation:

Simplifying
2a2 + -17a = -30

Reorder the terms:
-17a + 2a2 = -30

Solving
-17a + 2a2 = -30

Solving for variable 'a'.

Reorder the terms:
30 + -17a + 2a2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -17a + 2a2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {2.5, 6}