2(a)(a)-46a+252=0

Solution for 2(a)(a)-46a+252=0 equation:

Simplifying
2(a)(a) + -46a + 252 = 0

Multiply a * a
2a2 + -46a + 252 = 0

Reorder the terms:
252 + -46a + 2a2 = 0

Solving
252 + -46a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(126 + -23a + a2) = 0

Factor a trinomial.
2((9 + -1a)(14 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 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 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Subproblem 2
Set the factor '(14 + -1a)' equal to zero and attempt to solve:

Simplifying
14 + -1a = 0

Solving
14 + -1a = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1a = 0 + -14
-1a = 0 + -14

Combine like terms: 0 + -14 = -14
-1a = -14

Divide each side by '-1'.
a = 14

Simplifying
a = 14
Solution
a = {9, 14}