(50+X)(75+2X)=9375

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Solution for (50+X)(75+2X)=9375 equation: 


Simplifying
(50 + X)(75 + 2X) = 9375

Multiply (50 + X) * (75 + 2X)
(50(75 + 2X) + X(75 + 2X)) = 9375
((75 * 50 + 2X * 50) + X(75 + 2X)) = 9375
((3750 + 100X) + X(75 + 2X)) = 9375
(3750 + 100X + (75 * X + 2X * X)) = 9375
(3750 + 100X + (75X + 2X2)) = 9375

Combine like terms: 100X + 75X = 175X
(3750 + 175X + 2X2) = 9375

Solving
3750 + 175X + 2X2 = 9375

Solving for variable 'X'.

Reorder the terms:
3750 + -9375 + 175X + 2X2 = 9375 + -9375

Combine like terms: 3750 + -9375 = -5625
-5625 + 175X + 2X2 = 9375 + -9375

Combine like terms: 9375 + -9375 = 0
-5625 + 175X + 2X2 = 0

Factor a trinomial.
(-225 + -2X)(25 + -1X) = 0


Subproblem 1
Set the factor '(-225 + -2X)' equal to zero and attempt to solve:

Simplifying
-225 + -2X = 0

Solving
-225 + -2X = 0

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

Add '225' to each side of the equation.
-225 + 225 + -2X = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -2X = 0 + 225
-2X = 0 + 225

Combine like terms: 0 + 225 = 225
-2X = 225

Divide each side by '-2'.
X = -112.5

Simplifying
X = -112.5

Subproblem 2
Set the factor '(25 + -1X)' equal to zero and attempt to solve:

Simplifying
25 + -1X = 0

Solving
25 + -1X = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1X = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1X = 0 + -25
-1X = 0 + -25

Combine like terms: 0 + -25 = -25
-1X = -25

Divide each side by '-1'.
X = 25

Simplifying
X = 25
Solution
X = {-112.5, 25}

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