13X-X^2=40

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Solution for 13X-X^2=40 equation: 


Simplifying
13X + -1X2 = 40

Solving
13X + -1X2 = 40

Solving for variable 'X'.

Reorder the terms:
-40 + 13X + -1X2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 13X + -1X2 = 0

Factor a trinomial.
(-8 + X)(5 + -1X) = 0


Subproblem 1
Set the factor '(-8 + X)' equal to zero and attempt to solve:

Simplifying
-8 + X = 0

Solving
-8 + X = 0

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

Add '8' to each side of the equation.
-8 + 8 + X = 0 + 8

Combine like terms: -8 + 8 = 0
0 + X = 0 + 8
X = 0 + 8

Combine like terms: 0 + 8 = 8
X = 8

Simplifying
X = 8

Subproblem 2
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
Solution
X = {8, 5}

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