a^2-4a=30+3a

Solution for a^2-4a=30+3a equation:

Simplifying
a2 + -4a = 30 + 3a

Reorder the terms:
-4a + a2 = 30 + 3a

Solving
-4a + a2 = 30 + 3a

Solving for variable 'a'.

Reorder the terms:
-30 + -4a + -3a + a2 = 30 + 3a + -30 + -3a

Combine like terms: -4a + -3a = -7a
-30 + -7a + a2 = 30 + 3a + -30 + -3a

Reorder the terms:
-30 + -7a + a2 = 30 + -30 + 3a + -3a

Combine like terms: 30 + -30 = 0
-30 + -7a + a2 = 0 + 3a + -3a
-30 + -7a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-30 + -7a + a2 = 0

Factor a trinomial.
(-3 + -1a)(10 + -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 '(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 = {-3, 10}