-49a^2+4606a-52000=42080

Solution for -49a^2+4606a-52000=42080 equation:

Simplifying
-49a2 + 4606a + -52000 = 42080

Reorder the terms:
-52000 + 4606a + -49a2 = 42080

Solving
-52000 + 4606a + -49a2 = 42080

Solving for variable 'a'.

Reorder the terms:
-52000 + -42080 + 4606a + -49a2 = 42080 + -42080

Combine like terms: -52000 + -42080 = -94080
-94080 + 4606a + -49a2 = 42080 + -42080

Combine like terms: 42080 + -42080 = 0
-94080 + 4606a + -49a2 = 0

Factor out the Greatest Common Factor (GCF), '49'.
49(-1920 + 94a + -1a2) = 0

Factor a trinomial.
49((-64 + a)(30 + -1a)) = 0

Ignore the factor 49.
Subproblem 1
Set the factor '(-64 + a)' equal to zero and attempt to solve:

Simplifying
-64 + a = 0

Solving
-64 + a = 0

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

Add '64' to each side of the equation.
-64 + 64 + a = 0 + 64

Combine like terms: -64 + 64 = 0
0 + a = 0 + 64
a = 0 + 64

Combine like terms: 0 + 64 = 64
a = 64

Simplifying
a = 64
Subproblem 2
Set the factor '(30 + -1a)' equal to zero and attempt to solve:

Simplifying
30 + -1a = 0

Solving
30 + -1a = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1a = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1a = 0 + -30
-1a = 0 + -30

Combine like terms: 0 + -30 = -30
-1a = -30

Divide each side by '-1'.
a = 30

Simplifying
a = 30
Solution
a = {64, 30}