-x^4+4x^3=7x^2

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Solution for -x^4+4x^3=7x^2 equation: 


Simplifying
-1x4 + 4x3 = 7x2

Reorder the terms:
4x3 + -1x4 = 7x2

Solving
4x3 + -1x4 = 7x2

Solving for variable 'x'.

Reorder the terms:
-7x2 + 4x3 + -1x4 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-7x2 + 4x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-7 + 4x + -1x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

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

Subproblem 2
Set the factor '(-7 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
-7 + 4x + -1x2 = 0

Solving
-7 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
7 + -4x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -4x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -4x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x + x2 = 0 + -7
-4x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-4x + x2 = -7

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -7 + 4

Reorder the terms:
4 + -4x + x2 = -7 + 4

Combine like terms: -7 + 4 = -3
4 + -4x + x2 = -3

Factor a perfect square on the left side:
(x + -2)(x + -2) = -3

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
x = {0}

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