(40-X)(3X+90)=3600

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Solution for (40-X)(3X+90)=3600 equation: 


Simplifying
(40 + -1X)(3X + 90) = 3600

Reorder the terms:
(40 + -1X)(90 + 3X) = 3600

Multiply (40 + -1X) * (90 + 3X)
(40(90 + 3X) + -1X * (90 + 3X)) = 3600
((90 * 40 + 3X * 40) + -1X * (90 + 3X)) = 3600
((3600 + 120X) + -1X * (90 + 3X)) = 3600
(3600 + 120X + (90 * -1X + 3X * -1X)) = 3600
(3600 + 120X + (-90X + -3X2)) = 3600

Combine like terms: 120X + -90X = 30X
(3600 + 30X + -3X2) = 3600

Add '-3600' to each side of the equation.
3600 + 30X + -3600 + -3X2 = 3600 + -3600

Reorder the terms:
3600 + -3600 + 30X + -3X2 = 3600 + -3600

Combine like terms: 3600 + -3600 = 0
0 + 30X + -3X2 = 3600 + -3600
30X + -3X2 = 3600 + -3600

Combine like terms: 3600 + -3600 = 0
30X + -3X2 = 0

Solving
30X + -3X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3X'.
3X(10 + -1X) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0

Subproblem 2
Set the factor '(10 + -1X)' equal to zero and attempt to solve:

Simplifying
10 + -1X = 0

Solving
10 + -1X = 0

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

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

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

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

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

Simplifying
X = 10
Solution
X = {0, 10}

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