a(12a+5)=7

Solution for a(12a+5)=7 equation:

Simplifying
a(12a + 5) = 7

Reorder the terms:
a(5 + 12a) = 7
(5 * a + 12a * a) = 7
(5a + 12a2) = 7

Solving
5a + 12a2 = 7

Solving for variable 'a'.

Reorder the terms:
-7 + 5a + 12a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 5a + 12a2 = 0

Factor a trinomial.
(-1 + -1a)(7 + -12a) = 0

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 '(7 + -12a)' equal to zero and attempt to solve:

Simplifying
7 + -12a = 0

Solving
7 + -12a = 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 + -12a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -12a = 0 + -7
-12a = 0 + -7

Combine like terms: 0 + -7 = -7
-12a = -7

Divide each side by '-12'.
a = 0.5833333333

Simplifying
a = 0.5833333333
Solution
a = {-1, 0.5833333333}