-4x^6(10x+3x^2-7)=

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Solution for -4x^6(10x+3x^2-7)= equation: 


Simplifying
-4x6(10x + 3x2 + -7) = 0

Reorder the terms:
-4x6(-7 + 10x + 3x2) = 0
(-7 * -4x6 + 10x * -4x6 + 3x2 * -4x6) = 0
(28x6 + -40x7 + -12x8) = 0

Solving
28x6 + -40x7 + -12x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x6'.
4x6(7 + -10x + -3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve:

Simplifying
x6 = 0

Solving
x6 = 0

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

Simplifying
x6 = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(7 + -10x + -3x2)' equal to zero and attempt to solve:

Simplifying
7 + -10x + -3x2 = 0

Solving
7 + -10x + -3x2 = 0

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

Divide each side by '-3'.
-2.333333333 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 3.333333333x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 3.333333333x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 2.333333333
3.333333333x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
3.333333333x + x2 = 2.333333333

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 2.333333333 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 2.333333333 + 2.777777779

Combine like terms: 2.333333333 + 2.777777779 = 5.111111112
2.777777779 + 3.333333333x + x2 = 5.111111112

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 5.111111112

Calculate the square root of the right side: 2.260776661

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.260776661 and -2.260776661.


Subproblem 1
x + 1.666666667 = 2.260776661

Simplifying
x + 1.666666667 = 2.260776661

Reorder the terms:
1.666666667 + x = 2.260776661

Solving
1.666666667 + x = 2.260776661

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 2.260776661 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.260776661 + -1.666666667
x = 2.260776661 + -1.666666667

Combine like terms: 2.260776661 + -1.666666667 = 0.594109994
x = 0.594109994

Simplifying
x = 0.594109994


Subproblem 2
x + 1.666666667 = -2.260776661

Simplifying
x + 1.666666667 = -2.260776661

Reorder the terms:
1.666666667 + x = -2.260776661

Solving
1.666666667 + x = -2.260776661

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -2.260776661 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.260776661 + -1.666666667
x = -2.260776661 + -1.666666667

Combine like terms: -2.260776661 + -1.666666667 = -3.927443328
x = -3.927443328

Simplifying
x = -3.927443328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.594109994, -3.927443328}
Solution
x = {0.594109994, -3.927443328}

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