4(-174+23a+a^2)=0

Solution for 4(-174+23a+a^2)=0 equation:

Simplifying
4(-174 + 23a + a2) = 0
(-174 * 4 + 23a * 4 + a2 * 4) = 0
(-696 + 92a + 4a2) = 0

Solving
-696 + 92a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-174 + 23a + a2) = 0

Factor a trinomial.
4((-29 + -1a)(6 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-29 + -1a)' equal to zero and attempt to solve:

Simplifying
-29 + -1a = 0

Solving
-29 + -1a = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1a = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1a = 0 + 29
-1a = 0 + 29

Combine like terms: 0 + 29 = 29
-1a = 29

Divide each side by '-1'.
a = -29

Simplifying
a = -29
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-29, 6}