10=a(a-9)

Solution for 10=a(a-9) equation:

Simplifying
10 = a(a + -9)

Reorder the terms:
10 = a(-9 + a)
10 = (-9 * a + a * a)
10 = (-9a + a2)

Solving
10 = -9a + a2

Solving for variable 'a'.

Reorder the terms:
10 + 9a + -1a2 = -9a + 9a + a2 + -1a2

Combine like terms: -9a + 9a = 0
10 + 9a + -1a2 = 0 + a2 + -1a2
10 + 9a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
10 + 9a + -1a2 = 0

Factor a trinomial.
(10 + -1a)(1 + a) = 0

Subproblem 1
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 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 + a = 0 + -1

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

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

Simplifying
a = -1
Solution
a = {10, -1}