4a^2-15a-65=a

Solution for 4a^2-15a-65=a equation:

Simplifying
4a2 + -15a + -65 = a

Reorder the terms:
-65 + -15a + 4a2 = a

Solving
-65 + -15a + 4a2 = a

Solving for variable 'a'.

Reorder the terms:
-65 + -15a + -1a + 4a2 = a + -1a

Combine like terms: -15a + -1a = -16a
-65 + -16a + 4a2 = a + -1a

Combine like terms: a + -1a = 0
-65 + -16a + 4a2 = 0

Factor a trinomial.
(-5 + -2a)(13 + -2a) = 0

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

Simplifying
-5 + -2a = 0

Solving
-5 + -2a = 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 + -2a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5

Combine like terms: 0 + 5 = 5
-2a = 5

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 2
Set the factor '(13 + -2a)' equal to zero and attempt to solve:

Simplifying
13 + -2a = 0

Solving
13 + -2a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2a = 0 + -13
-2a = 0 + -13

Combine like terms: 0 + -13 = -13
-2a = -13

Divide each side by '-2'.
a = 6.5

Simplifying
a = 6.5
Solution
a = {-2.5, 6.5}