7=-a^2+4a+4

Solution for 7=-a^2+4a+4 equation:

Simplifying
7 = -1a2 + 4a + 4

Reorder the terms:
7 = 4 + 4a + -1a2

Solving
7 = 4 + 4a + -1a2

Solving for variable 'a'.

Combine like terms: 7 + -4 = 3
3 + -4a + a2 = 4 + 4a + -1a2 + -4 + -4a + a2

Reorder the terms:
3 + -4a + a2 = 4 + -4 + 4a + -4a + -1a2 + a2

Combine like terms: 4 + -4 = 0
3 + -4a + a2 = 0 + 4a + -4a + -1a2 + a2
3 + -4a + a2 = 4a + -4a + -1a2 + a2

Combine like terms: 4a + -4a = 0
3 + -4a + a2 = 0 + -1a2 + a2
3 + -4a + a2 = -1a2 + a2

Combine like terms: -1a2 + a2 = 0
3 + -4a + a2 = 0

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Subproblem 2
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
Solution
a = {1, 3}