9600=(60+2x)(20-6x)

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Solution for 9600=(60+2x)(20-6x) equation: 


Simplifying
9600 = (60 + 2x)(20 + -6x)

Multiply (60 + 2x) * (20 + -6x)
9600 = (60(20 + -6x) + 2x * (20 + -6x))
9600 = ((20 * 60 + -6x * 60) + 2x * (20 + -6x))
9600 = ((1200 + -360x) + 2x * (20 + -6x))
9600 = (1200 + -360x + (20 * 2x + -6x * 2x))
9600 = (1200 + -360x + (40x + -12x2))

Combine like terms: -360x + 40x = -320x
9600 = (1200 + -320x + -12x2)

Solving
9600 = 1200 + -320x + -12x2

Solving for variable 'x'.

Combine like terms: 9600 + -1200 = 8400
8400 + 320x + 12x2 = 1200 + -320x + -12x2 + -1200 + 320x + 12x2

Reorder the terms:
8400 + 320x + 12x2 = 1200 + -1200 + -320x + 320x + -12x2 + 12x2

Combine like terms: 1200 + -1200 = 0
8400 + 320x + 12x2 = 0 + -320x + 320x + -12x2 + 12x2
8400 + 320x + 12x2 = -320x + 320x + -12x2 + 12x2

Combine like terms: -320x + 320x = 0
8400 + 320x + 12x2 = 0 + -12x2 + 12x2
8400 + 320x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
8400 + 320x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2100 + 80x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2100 + 80x + 3x2)' equal to zero and attempt to solve:

Simplifying
2100 + 80x + 3x2 = 0

Solving
2100 + 80x + 3x2 = 0

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

Divide each side by '3'.
700 + 26.66666667x + x2 = 0

Move the constant term to the right:

Add '-700' to each side of the equation.
700 + 26.66666667x + -700 + x2 = 0 + -700

Reorder the terms:
700 + -700 + 26.66666667x + x2 = 0 + -700

Combine like terms: 700 + -700 = 0
0 + 26.66666667x + x2 = 0 + -700
26.66666667x + x2 = 0 + -700

Combine like terms: 0 + -700 = -700
26.66666667x + x2 = -700

The x term is 26.66666667x.  Take half its coefficient (13.33333334).
Square it (177.7777780) and add it to both sides.

Add '177.7777780' to each side of the equation.
26.66666667x + 177.7777780 + x2 = -700 + 177.7777780

Reorder the terms:
177.7777780 + 26.66666667x + x2 = -700 + 177.7777780

Combine like terms: -700 + 177.7777780 = -522.222222
177.7777780 + 26.66666667x + x2 = -522.222222

Factor a perfect square on the left side:
(x + 13.33333334)(x + 13.33333334) = -522.222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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