2a(7a+6)=2

Solution for 2a(7a+6)=2 equation:

Simplifying
2a(7a + 6) = 2

Reorder the terms:
2a(6 + 7a) = 2
(6 * 2a + 7a * 2a) = 2
(12a + 14a2) = 2

Solving
12a + 14a2 = 2

Solving for variable 'a'.

Reorder the terms:
-2 + 12a + 14a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 12a + 14a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 6a + 7a2) = 0

Factor a trinomial.
2((-1 + -1a)(1 + -7a)) = 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 '(1 + -7a)' equal to zero and attempt to solve:

Simplifying
1 + -7a = 0

Solving
1 + -7a = 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 + -7a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7a = 0 + -1
-7a = 0 + -1

Combine like terms: 0 + -1 = -1
-7a = -1

Divide each side by '-7'.
a = 0.1428571429

Simplifying
a = 0.1428571429
Solution
a = {-1, 0.1428571429}