14a^2+7a-196=0

Solution for 14a^2+7a-196=0 equation:

Simplifying
14a2 + 7a + -196 = 0

Reorder the terms:
-196 + 7a + 14a2 = 0

Solving
-196 + 7a + 14a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-28 + a + 2a2) = 0

Factor a trinomial.
7((-4 + -1a)(7 + -2a)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

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

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

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-4, 3.5}