10a^2=22a-4

Solution for 10a^2=22a-4 equation:

Simplifying
10a2 = 22a + -4

Reorder the terms:
10a2 = -4 + 22a

Solving
10a2 = -4 + 22a

Solving for variable 'a'.

Reorder the terms:
4 + -22a + 10a2 = -4 + 22a + 4 + -22a

Reorder the terms:
4 + -22a + 10a2 = -4 + 4 + 22a + -22a

Combine like terms: -4 + 4 = 0
4 + -22a + 10a2 = 0 + 22a + -22a
4 + -22a + 10a2 = 22a + -22a

Combine like terms: 22a + -22a = 0
4 + -22a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -11a + 5a2) = 0

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

Ignore the factor 2.
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 '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {0.2, 2}