45=x(14-x)

Solution for 45=x(14-x) equation:

Simplifying
45 = x(14 + -1x)
45 = (14 * x + -1x * x)
45 = (14x + -1x2)

Solving
45 = 14x + -1x2

Solving for variable 'x'.

Reorder the terms:
45 + -14x + x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
45 + -14x + x2 = 0 + -1x2 + x2
45 + -14x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
45 + -14x + x2 = 0

Factor a trinomial.
(5 + -1x)(9 + -1x) = 0

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {5, 9}