a^2=9a-14

Solution for a^2=9a-14 equation:

Simplifying
a2 = 9a + -14

Reorder the terms:
a2 = -14 + 9a

Solving
a2 = -14 + 9a

Solving for variable 'a'.

Reorder the terms:
14 + -9a + a2 = -14 + 9a + 14 + -9a

Reorder the terms:
14 + -9a + a2 = -14 + 14 + 9a + -9a

Combine like terms: -14 + 14 = 0
14 + -9a + a2 = 0 + 9a + -9a
14 + -9a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
14 + -9a + a2 = 0

Factor a trinomial.
(2 + -1a)(7 + -1a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, 7}