400=2a^2-8a+16

Solution for 400=2a^2-8a+16 equation:

Simplifying
400 = 2a2 + -8a + 16

Reorder the terms:
400 = 16 + -8a + 2a2

Solving
400 = 16 + -8a + 2a2

Solving for variable 'a'.

Combine like terms: 400 + -16 = 384
384 + 8a + -2a2 = 16 + -8a + 2a2 + -16 + 8a + -2a2

Reorder the terms:
384 + 8a + -2a2 = 16 + -16 + -8a + 8a + 2a2 + -2a2

Combine like terms: 16 + -16 = 0
384 + 8a + -2a2 = 0 + -8a + 8a + 2a2 + -2a2
384 + 8a + -2a2 = -8a + 8a + 2a2 + -2a2

Combine like terms: -8a + 8a = 0
384 + 8a + -2a2 = 0 + 2a2 + -2a2
384 + 8a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
384 + 8a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(192 + 4a + -1a2) = 0

Factor a trinomial.
2((16 + -1a)(12 + a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -1a)' equal to zero and attempt to solve:

Simplifying
16 + -1a = 0

Solving
16 + -1a = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1a = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1a = 0 + -16
-1a = 0 + -16

Combine like terms: 0 + -16 = -16
-1a = -16

Divide each side by '-1'.
a = 16

Simplifying
a = 16
Subproblem 2
Set the factor '(12 + a)' equal to zero and attempt to solve:

Simplifying
12 + a = 0

Solving
12 + a = 0

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

Add '-12' to each side of the equation.
12 + -12 + a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + a = 0 + -12
a = 0 + -12

Combine like terms: 0 + -12 = -12
a = -12

Simplifying
a = -12
Solution
a = {16, -12}