10a^2=11a-3

Solution for 10a^2=11a-3 equation:

Simplifying
10a2 = 11a + -3

Reorder the terms:
10a2 = -3 + 11a

Solving
10a2 = -3 + 11a

Solving for variable 'a'.

Reorder the terms:
3 + -11a + 10a2 = -3 + 11a + 3 + -11a

Reorder the terms:
3 + -11a + 10a2 = -3 + 3 + 11a + -11a

Combine like terms: -3 + 3 = 0
3 + -11a + 10a2 = 0 + 11a + -11a
3 + -11a + 10a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
3 + -11a + 10a2 = 0

Factor a trinomial.
(1 + -2a)(3 + -5a) = 0

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

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

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

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Subproblem 2
Set the factor '(3 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

Solving
3 + -5a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5a = 0 + -3
-5a = 0 + -3

Combine like terms: 0 + -3 = -3
-5a = -3

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {0.5, 0.6}