10a^2-50a-a+5=0

Solution for 10a^2-50a-a+5=0 equation:

Simplifying
10a2 + -50a + -1a + 5 = 0

Reorder the terms:
5 + -50a + -1a + 10a2 = 0

Combine like terms: -50a + -1a = -51a
5 + -51a + 10a2 = 0

Solving
5 + -51a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -10a)(5 + -1a) = 0

Subproblem 1
Set the factor '(1 + -10a)' equal to zero and attempt to solve:

Simplifying
1 + -10a = 0

Solving
1 + -10a = 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 + -10a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10a = 0 + -1
-10a = 0 + -1

Combine like terms: 0 + -1 = -1
-10a = -1

Divide each side by '-10'.
a = 0.1

Simplifying
a = 0.1
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {0.1, 5}