x^4+x^3=2x^2

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


Simplifying
x4 + x3 = 2x2

Reorder the terms:
x3 + x4 = 2x2

Solving
x3 + x4 = 2x2

Solving for variable 'x'.

Reorder the terms:
-2x2 + x3 + x4 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2x2 + x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-2 + x + x2) = 0

Factor a trinomial.
x2((-2 + -1x)(1 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -2, 1}

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