7v^3-10v^2=9v^4

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Solution for 7v^3-10v^2=9v^4 equation: 


Simplifying
7v3 + -10v2 = 9v4

Reorder the terms:
-10v2 + 7v3 = 9v4

Solving
-10v2 + 7v3 = 9v4

Solving for variable 'v'.

Combine like terms: 9v4 + -9v4 = 0
-10v2 + 7v3 + -9v4 = 0

Factor out the Greatest Common Factor (GCF), 'v2'.
v2(-10 + 7v + -9v2) = 0


Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}

Subproblem 2
Set the factor '(-10 + 7v + -9v2)' equal to zero and attempt to solve:

Simplifying
-10 + 7v + -9v2 = 0

Solving
-10 + 7v + -9v2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
1.111111111 + -0.7777777778v + v2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -0.7777777778v + -1.111111111 + v2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -0.7777777778v + v2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -0.7777777778v + v2 = 0 + -1.111111111
-0.7777777778v + v2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-0.7777777778v + v2 = -1.111111111

The v term is -0.7777777778v.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778v + 0.1512345679 + v2 = -1.111111111 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778v + v2 = -1.111111111 + 0.1512345679

Combine like terms: -1.111111111 + 0.1512345679 = -0.9598765431
0.1512345679 + -0.7777777778v + v2 = -0.9598765431

Factor a perfect square on the left side:
(v + -0.3888888889)(v + -0.3888888889) = -0.9598765431

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.
Solution
v = {0}

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