100=a^2-6a+9

Solution for 100=a^2-6a+9 equation:

Simplifying
100 = a2 + -6a + 9

Reorder the terms:
100 = 9 + -6a + a2

Solving
100 = 9 + -6a + a2

Solving for variable 'a'.

Combine like terms: 100 + -9 = 91
91 + 6a + -1a2 = 9 + -6a + a2 + -9 + 6a + -1a2

Reorder the terms:
91 + 6a + -1a2 = 9 + -9 + -6a + 6a + a2 + -1a2

Combine like terms: 9 + -9 = 0
91 + 6a + -1a2 = 0 + -6a + 6a + a2 + -1a2
91 + 6a + -1a2 = -6a + 6a + a2 + -1a2

Combine like terms: -6a + 6a = 0
91 + 6a + -1a2 = 0 + a2 + -1a2
91 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
91 + 6a + -1a2 = 0

Factor a trinomial.
(13 + -1a)(7 + a) = 0

Subproblem 1
Set the factor '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 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 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
Solution
a = {13, -7}