40a^2-2a-38=0

Solution for 40a^2-2a-38=0 equation:

Simplifying
40a2 + -2a + -38 = 0

Reorder the terms:
-38 + -2a + 40a2 = 0

Solving
-38 + -2a + 40a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -1a + 20a2) = 0

Factor a trinomial.
2((-19 + -20a)(1 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + -20a)' equal to zero and attempt to solve:

Simplifying
-19 + -20a = 0

Solving
-19 + -20a = 0

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

Add '19' to each side of the equation.
-19 + 19 + -20a = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -20a = 0 + 19
-20a = 0 + 19

Combine like terms: 0 + 19 = 19
-20a = 19

Divide each side by '-20'.
a = -0.95

Simplifying
a = -0.95
Subproblem 2
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
Solution
a = {-0.95, 1}