5a^2-6a+7a^2+3a=

Solution for 5a^2-6a+7a^2+3a= equation:

Simplifying
5a2 + -6a + 7a2 + 3a = 0

Reorder the terms:
-6a + 3a + 5a2 + 7a2 = 0

Combine like terms: -6a + 3a = -3a
-3a + 5a2 + 7a2 = 0

Combine like terms: 5a2 + 7a2 = 12a2
-3a + 12a2 = 0

Solving
-3a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-1 + 4a) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-1 + 4a)' equal to zero and attempt to solve:

Simplifying
-1 + 4a = 0

Solving
-1 + 4a = 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 + 4a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4a = 0 + 1
4a = 0 + 1

Combine like terms: 0 + 1 = 1
4a = 1

Divide each side by '4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {0, 0.25}