10(3x^2-7)=10000(2x+4)

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Solution for 10(3x^2-7)=10000(2x+4) equation: 


Simplifying
10(3x2 + -7) = 10000(2x + 4)

Reorder the terms:
10(-7 + 3x2) = 10000(2x + 4)
(-7 * 10 + 3x2 * 10) = 10000(2x + 4)
(-70 + 30x2) = 10000(2x + 4)

Reorder the terms:
-70 + 30x2 = 10000(4 + 2x)
-70 + 30x2 = (4 * 10000 + 2x * 10000)
-70 + 30x2 = (40000 + 20000x)

Solving
-70 + 30x2 = 40000 + 20000x

Solving for variable 'x'.

Reorder the terms:
-70 + -40000 + -20000x + 30x2 = 40000 + 20000x + -40000 + -20000x

Combine like terms: -70 + -40000 = -40070
-40070 + -20000x + 30x2 = 40000 + 20000x + -40000 + -20000x

Reorder the terms:
-40070 + -20000x + 30x2 = 40000 + -40000 + 20000x + -20000x

Combine like terms: 40000 + -40000 = 0
-40070 + -20000x + 30x2 = 0 + 20000x + -20000x
-40070 + -20000x + 30x2 = 20000x + -20000x

Combine like terms: 20000x + -20000x = 0
-40070 + -20000x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-4007 + -2000x + 3x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-4007 + -2000x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4007 + -2000x + 3x2 = 0

Solving
-4007 + -2000x + 3x2 = 0

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

Divide each side by '3'.
-1335.666667 + -666.6666667x + x2 = 0

Move the constant term to the right:

Add '1335.666667' to each side of the equation.
-1335.666667 + -666.6666667x + 1335.666667 + x2 = 0 + 1335.666667

Reorder the terms:
-1335.666667 + 1335.666667 + -666.6666667x + x2 = 0 + 1335.666667

Combine like terms: -1335.666667 + 1335.666667 = 0.000000
0.000000 + -666.6666667x + x2 = 0 + 1335.666667
-666.6666667x + x2 = 0 + 1335.666667

Combine like terms: 0 + 1335.666667 = 1335.666667
-666.6666667x + x2 = 1335.666667

The x term is -666.6666667x.  Take half its coefficient (-333.3333334).
Square it (111111.1112) and add it to both sides.

Add '111111.1112' to each side of the equation.
-666.6666667x + 111111.1112 + x2 = 1335.666667 + 111111.1112

Reorder the terms:
111111.1112 + -666.6666667x + x2 = 1335.666667 + 111111.1112

Combine like terms: 1335.666667 + 111111.1112 = 112446.777867
111111.1112 + -666.6666667x + x2 = 112446.777867

Factor a perfect square on the left side:
(x + -333.3333334)(x + -333.3333334) = 112446.777867

Calculate the square root of the right side: 335.330848368

Break this problem into two subproblems by setting 
(x + -333.3333334) equal to 335.330848368 and -335.330848368.


Subproblem 1
x + -333.3333334 = 335.330848368

Simplifying
x + -333.3333334 = 335.330848368

Reorder the terms:
-333.3333334 + x = 335.330848368

Solving
-333.3333334 + x = 335.330848368

Solving for variable 'x'.

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

Add '333.3333334' to each side of the equation.
-333.3333334 + 333.3333334 + x = 335.330848368 + 333.3333334

Combine like terms: -333.3333334 + 333.3333334 = 0.0000000
0.0000000 + x = 335.330848368 + 333.3333334
x = 335.330848368 + 333.3333334

Combine like terms: 335.330848368 + 333.3333334 = 668.664181768
x = 668.664181768

Simplifying
x = 668.664181768


Subproblem 2
x + -333.3333334 = -335.330848368

Simplifying
x + -333.3333334 = -335.330848368

Reorder the terms:
-333.3333334 + x = -335.330848368

Solving
-333.3333334 + x = -335.330848368

Solving for variable 'x'.

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

Add '333.3333334' to each side of the equation.
-333.3333334 + 333.3333334 + x = -335.330848368 + 333.3333334

Combine like terms: -333.3333334 + 333.3333334 = 0.0000000
0.0000000 + x = -335.330848368 + 333.3333334
x = -335.330848368 + 333.3333334

Combine like terms: -335.330848368 + 333.3333334 = -1.997514968
x = -1.997514968

Simplifying
x = -1.997514968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {668.664181768, -1.997514968}
Solution
x = {668.664181768, -1.997514968}

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