10a^2+6a-4=0

Solution for 10a^2+6a-4=0 equation:

Simplifying
10a2 + 6a + -4 = 0

Reorder the terms:
-4 + 6a + 10a2 = 0

Solving
-4 + 6a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3a + 5a2) = 0

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

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

Simplifying
-1 + -1a = 0

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

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

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

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

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

Simplifying
2 + -5a = 0

Solving
2 + -5a = 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 + -5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a = 0 + -2
-5a = 0 + -2

Combine like terms: 0 + -2 = -2
-5a = -2

Divide each side by '-5'.
a = 0.4

Simplifying
a = 0.4
Solution
a = {-1, 0.4}