a^2=7a-10

Solution for a^2=7a-10 equation:

Simplifying
a2 = 7a + -10

Reorder the terms:
a2 = -10 + 7a

Solving
a2 = -10 + 7a

Solving for variable 'a'.

Reorder the terms:
10 + -7a + a2 = -10 + 7a + 10 + -7a

Reorder the terms:
10 + -7a + a2 = -10 + 10 + 7a + -7a

Combine like terms: -10 + 10 = 0
10 + -7a + a2 = 0 + 7a + -7a
10 + -7a + a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
10 + -7a + a2 = 0

Factor a trinomial.
(2 + -1a)(5 + -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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {2, 5}