(150-2X)(100-2X)=0

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Solution for (150-2X)(100-2X)=0 equation: 


Simplifying
(150 + -2X)(100 + -2X) = 0

Multiply (150 + -2X) * (100 + -2X)
(150(100 + -2X) + -2X * (100 + -2X)) = 0
((100 * 150 + -2X * 150) + -2X * (100 + -2X)) = 0
((15000 + -300X) + -2X * (100 + -2X)) = 0
(15000 + -300X + (100 * -2X + -2X * -2X)) = 0
(15000 + -300X + (-200X + 4X2)) = 0

Combine like terms: -300X + -200X = -500X
(15000 + -500X + 4X2) = 0

Solving
15000 + -500X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3750 + -125X + X2) = 0

Factor a trinomial.
4((50 + -1X)(75 + -1X)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50 + -1X)' equal to zero and attempt to solve:

Simplifying
50 + -1X = 0

Solving
50 + -1X = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1X = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1X = 0 + -50
-1X = 0 + -50

Combine like terms: 0 + -50 = -50
-1X = -50

Divide each side by '-1'.
X = 50

Simplifying
X = 50

Subproblem 2
Set the factor '(75 + -1X)' equal to zero and attempt to solve:

Simplifying
75 + -1X = 0

Solving
75 + -1X = 0

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

Add '-75' to each side of the equation.
75 + -75 + -1X = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -1X = 0 + -75
-1X = 0 + -75

Combine like terms: 0 + -75 = -75
-1X = -75

Divide each side by '-1'.
X = 75

Simplifying
X = 75
Solution
X = {50, 75}

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