7a*a+20a+12=0

Solution for 7a*a+20a+12=0 equation:

Simplifying
7a * a + 20a + 12 = 0

Multiply a * a
7a2 + 20a + 12 = 0

Reorder the terms:
12 + 20a + 7a2 = 0

Solving
12 + 20a + 7a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + a)(6 + 7a) = 0

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

Simplifying
2 + a = 0

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

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

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

Simplifying
a = -2
Subproblem 2
Set the factor '(6 + 7a)' equal to zero and attempt to solve:

Simplifying
6 + 7a = 0

Solving
6 + 7a = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7a = 0 + -6
7a = 0 + -6

Combine like terms: 0 + -6 = -6
7a = -6

Divide each side by '7'.
a = -0.8571428571

Simplifying
a = -0.8571428571
Solution
a = {-2, -0.8571428571}