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.
(-7 + -1a)(4 + -1a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {-7, 4}