a^2-a=3a+21

Solution for a^2-a=3a+21 equation:

Simplifying
a2 + -1a = 3a + 21

Reorder the terms:
-1a + a2 = 3a + 21

Reorder the terms:
-1a + a2 = 21 + 3a

Solving
-1a + a2 = 21 + 3a

Solving for variable 'a'.

Reorder the terms:
-21 + -1a + -3a + a2 = 21 + 3a + -21 + -3a

Combine like terms: -1a + -3a = -4a
-21 + -4a + a2 = 21 + 3a + -21 + -3a

Reorder the terms:
-21 + -4a + a2 = 21 + -21 + 3a + -3a

Combine like terms: 21 + -21 = 0
-21 + -4a + a2 = 0 + 3a + -3a
-21 + -4a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-21 + -4a + a2 = 0

Factor a trinomial.
(-3 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-3, 7}