a^2-2a=40+4a

Solution for a^2-2a=40+4a equation:

Simplifying
a2 + -2a = 40 + 4a

Reorder the terms:
-2a + a2 = 40 + 4a

Solving
-2a + a2 = 40 + 4a

Solving for variable 'a'.

Reorder the terms:
-40 + -2a + -4a + a2 = 40 + 4a + -40 + -4a

Combine like terms: -2a + -4a = -6a
-40 + -6a + a2 = 40 + 4a + -40 + -4a

Reorder the terms:
-40 + -6a + a2 = 40 + -40 + 4a + -4a

Combine like terms: 40 + -40 = 0
-40 + -6a + a2 = 0 + 4a + -4a
-40 + -6a + a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-40 + -6a + a2 = 0

Factor a trinomial.
(-4 + -1a)(10 + -1a) = 0

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

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {-4, 10}