a^2=28+3a

Solution for a^2=28+3a equation:

Simplifying
a2 = 28 + 3a

Solving
a2 = 28 + 3a

Solving for variable 'a'.

Reorder the terms:
-28 + -3a + a2 = 28 + 3a + -28 + -3a

Reorder the terms:
-28 + -3a + a2 = 28 + -28 + 3a + -3a

Combine like terms: 28 + -28 = 0
-28 + -3a + a2 = 0 + 3a + -3a
-28 + -3a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-28 + -3a + a2 = 0

Factor a trinomial.
(-4 + -1a)(7 + -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 '(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 = {-4, 7}