a(14a+5)=9

Solution for a(14a+5)=9 equation:

Simplifying
a(14a + 5) = 9

Reorder the terms:
a(5 + 14a) = 9
(5 * a + 14a * a) = 9
(5a + 14a2) = 9

Solving
5a + 14a2 = 9

Solving for variable 'a'.

Reorder the terms:
-9 + 5a + 14a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 5a + 14a2 = 0

Factor a trinomial.
(-1 + -1a)(9 + -14a) = 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 '(9 + -14a)' equal to zero and attempt to solve:

Simplifying
9 + -14a = 0

Solving
9 + -14a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -14a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -14a = 0 + -9
-14a = 0 + -9

Combine like terms: 0 + -9 = -9
-14a = -9

Divide each side by '-14'.
a = 0.6428571429

Simplifying
a = 0.6428571429
Solution
a = {-1, 0.6428571429}