100x-4x^2=(30-2x)(25-2x)

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Solution for 100x-4x^2=(30-2x)(25-2x) equation: 


Simplifying
100x + -4x2 = (30 + -2x)(25 + -2x)

Multiply (30 + -2x) * (25 + -2x)
100x + -4x2 = (30(25 + -2x) + -2x * (25 + -2x))
100x + -4x2 = ((25 * 30 + -2x * 30) + -2x * (25 + -2x))
100x + -4x2 = ((750 + -60x) + -2x * (25 + -2x))
100x + -4x2 = (750 + -60x + (25 * -2x + -2x * -2x))
100x + -4x2 = (750 + -60x + (-50x + 4x2))

Combine like terms: -60x + -50x = -110x
100x + -4x2 = (750 + -110x + 4x2)

Solving
100x + -4x2 = 750 + -110x + 4x2

Solving for variable 'x'.

Reorder the terms:
-750 + 100x + 110x + -4x2 + -4x2 = 750 + -110x + 4x2 + -750 + 110x + -4x2

Combine like terms: 100x + 110x = 210x
-750 + 210x + -4x2 + -4x2 = 750 + -110x + 4x2 + -750 + 110x + -4x2

Combine like terms: -4x2 + -4x2 = -8x2
-750 + 210x + -8x2 = 750 + -110x + 4x2 + -750 + 110x + -4x2

Reorder the terms:
-750 + 210x + -8x2 = 750 + -750 + -110x + 110x + 4x2 + -4x2

Combine like terms: 750 + -750 = 0
-750 + 210x + -8x2 = 0 + -110x + 110x + 4x2 + -4x2
-750 + 210x + -8x2 = -110x + 110x + 4x2 + -4x2

Combine like terms: -110x + 110x = 0
-750 + 210x + -8x2 = 0 + 4x2 + -4x2
-750 + 210x + -8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-750 + 210x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-375 + 105x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-375 + 105x + -4x2)' equal to zero and attempt to solve:

Simplifying
-375 + 105x + -4x2 = 0

Solving
-375 + 105x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
93.75 + -26.25x + x2 = 0

Move the constant term to the right:

Add '-93.75' to each side of the equation.
93.75 + -26.25x + -93.75 + x2 = 0 + -93.75

Reorder the terms:
93.75 + -93.75 + -26.25x + x2 = 0 + -93.75

Combine like terms: 93.75 + -93.75 = 0.00
0.00 + -26.25x + x2 = 0 + -93.75
-26.25x + x2 = 0 + -93.75

Combine like terms: 0 + -93.75 = -93.75
-26.25x + x2 = -93.75

The x term is -26.25x.  Take half its coefficient (-13.125).
Square it (172.265625) and add it to both sides.

Add '172.265625' to each side of the equation.
-26.25x + 172.265625 + x2 = -93.75 + 172.265625

Reorder the terms:
172.265625 + -26.25x + x2 = -93.75 + 172.265625

Combine like terms: -93.75 + 172.265625 = 78.515625
172.265625 + -26.25x + x2 = 78.515625

Factor a perfect square on the left side:
(x + -13.125)(x + -13.125) = 78.515625

Calculate the square root of the right side: 8.860904299

Break this problem into two subproblems by setting 
(x + -13.125) equal to 8.860904299 and -8.860904299.


Subproblem 1
x + -13.125 = 8.860904299

Simplifying
x + -13.125 = 8.860904299

Reorder the terms:
-13.125 + x = 8.860904299

Solving
-13.125 + x = 8.860904299

Solving for variable 'x'.

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

Add '13.125' to each side of the equation.
-13.125 + 13.125 + x = 8.860904299 + 13.125

Combine like terms: -13.125 + 13.125 = 0.000
0.000 + x = 8.860904299 + 13.125
x = 8.860904299 + 13.125

Combine like terms: 8.860904299 + 13.125 = 21.985904299
x = 21.985904299

Simplifying
x = 21.985904299


Subproblem 2
x + -13.125 = -8.860904299

Simplifying
x + -13.125 = -8.860904299

Reorder the terms:
-13.125 + x = -8.860904299

Solving
-13.125 + x = -8.860904299

Solving for variable 'x'.

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

Add '13.125' to each side of the equation.
-13.125 + 13.125 + x = -8.860904299 + 13.125

Combine like terms: -13.125 + 13.125 = 0.000
0.000 + x = -8.860904299 + 13.125
x = -8.860904299 + 13.125

Combine like terms: -8.860904299 + 13.125 = 4.264095701
x = 4.264095701

Simplifying
x = 4.264095701


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.985904299, 4.264095701}
Solution
x = {21.985904299, 4.264095701}

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