6a^2+10a=3a+10

Solution for 6a^2+10a=3a+10 equation:

Simplifying
6a2 + 10a = 3a + 10

Reorder the terms:
10a + 6a2 = 3a + 10

Reorder the terms:
10a + 6a2 = 10 + 3a

Solving
10a + 6a2 = 10 + 3a

Solving for variable 'a'.

Reorder the terms:
-10 + 10a + -3a + 6a2 = 10 + 3a + -10 + -3a

Combine like terms: 10a + -3a = 7a
-10 + 7a + 6a2 = 10 + 3a + -10 + -3a

Reorder the terms:
-10 + 7a + 6a2 = 10 + -10 + 3a + -3a

Combine like terms: 10 + -10 = 0
-10 + 7a + 6a2 = 0 + 3a + -3a
-10 + 7a + 6a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-10 + 7a + 6a2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -6a)' equal to zero and attempt to solve:

Simplifying
5 + -6a = 0

Solving
5 + -6a = 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 + -6a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6a = 0 + -5
-6a = 0 + -5

Combine like terms: 0 + -5 = -5
-6a = -5

Divide each side by '-6'.
a = 0.8333333333

Simplifying
a = 0.8333333333
Solution
a = {-2, 0.8333333333}