(a-2)*(5-a)=

Solution for (a-2)*(5-a)= equation:

Simplifying
(a + -2)(5 + -1a) = 0

Reorder the terms:
(-2 + a)(5 + -1a) = 0

Multiply (-2 + a) * (5 + -1a)
(-2(5 + -1a) + a(5 + -1a)) = 0
((5 * -2 + -1a * -2) + a(5 + -1a)) = 0
((-10 + 2a) + a(5 + -1a)) = 0
(-10 + 2a + (5 * a + -1a * a)) = 0
(-10 + 2a + (5a + -1a2)) = 0

Combine like terms: 2a + 5a = 7a
(-10 + 7a + -1a2) = 0

Solving
-10 + 7a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-5 + a)' equal to zero and attempt to solve:

Simplifying
-5 + a = 0

Solving
-5 + a = 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 + a = 0 + 5

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

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

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