(150-2X)(100-2X)=10400

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Solution for (150-2X)(100-2X)=10400 equation: 


Simplifying
(150 + -2X)(100 + -2X) = 10400

Multiply (150 + -2X) * (100 + -2X)
(150(100 + -2X) + -2X * (100 + -2X)) = 10400
((100 * 150 + -2X * 150) + -2X * (100 + -2X)) = 10400
((15000 + -300X) + -2X * (100 + -2X)) = 10400
(15000 + -300X + (100 * -2X + -2X * -2X)) = 10400
(15000 + -300X + (-200X + 4X2)) = 10400

Combine like terms: -300X + -200X = -500X
(15000 + -500X + 4X2) = 10400

Solving
15000 + -500X + 4X2 = 10400

Solving for variable 'X'.

Reorder the terms:
15000 + -10400 + -500X + 4X2 = 10400 + -10400

Combine like terms: 15000 + -10400 = 4600
4600 + -500X + 4X2 = 10400 + -10400

Combine like terms: 10400 + -10400 = 0
4600 + -500X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1150 + -125X + X2) = 0

Factor a trinomial.
4((10 + -1X)(115 + -1X)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(115 + -1X)' equal to zero and attempt to solve:

Simplifying
115 + -1X = 0

Solving
115 + -1X = 0

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

Add '-115' to each side of the equation.
115 + -115 + -1X = 0 + -115

Combine like terms: 115 + -115 = 0
0 + -1X = 0 + -115
-1X = 0 + -115

Combine like terms: 0 + -115 = -115
-1X = -115

Divide each side by '-1'.
X = 115

Simplifying
X = 115
Solution
X = {10, 115}

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