2a^2-152a=810

Solution for 2a^2-152a=810 equation:

Simplifying
2a2 + -152a = 810

Reorder the terms:
-152a + 2a2 = 810

Solving
-152a + 2a2 = 810

Solving for variable 'a'.

Reorder the terms:
-810 + -152a + 2a2 = 810 + -810

Combine like terms: 810 + -810 = 0
-810 + -152a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-405 + -76a + a2) = 0

Factor a trinomial.
2((-5 + -1a)(81 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(81 + -1a)' equal to zero and attempt to solve:

Simplifying
81 + -1a = 0

Solving
81 + -1a = 0

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

Add '-81' to each side of the equation.
81 + -81 + -1a = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -1a = 0 + -81
-1a = 0 + -81

Combine like terms: 0 + -81 = -81
-1a = -81

Divide each side by '-1'.
a = 81

Simplifying
a = 81
Solution
a = {-5, 81}