(x^4+3x^3-2x^3)(-5x^2+x)=(x^4+3x^3-2x^3)(-5x^2)+(x+3x^3-2x^3)(x)

Solution for (x^4+3x^3-2x^3)(-5x^2+x)=(x^4+3x^3-2x^3)(-5x^2)+(x+3x^3-2x^3)(x) equation:

Simplifying
(x4 + 3x3 + -2x3)(-5x2 + x) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Reorder the terms:
(3x3 + -2x3 + x4)(-5x2 + x) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Combine like terms: 3x3 + -2x3 = 1x3
(1x3 + x4)(-5x2 + x) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Reorder the terms:
(1x3 + x4)(x + -5x2) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Multiply (1x3 + x4) * (x + -5x2)
(1x3 * (x + -5x2) + x4(x + -5x2)) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)
((x * 1x3 + -5x2 * 1x3) + x4(x + -5x2)) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)
((1x4 + -5x5) + x4(x + -5x2)) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)
(1x4 + -5x5 + (x * x4 + -5x2 * x4)) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)
(1x4 + -5x5 + (x5 + -5x6)) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Combine like terms: -5x5 + x5 = -4x5
(1x4 + -4x5 + -5x6) = (x4 + 3x3 + -2x3)(-5x2) + (x + 3x3 + -2x3)(x)

Reorder the terms:
1x4 + -4x5 + -5x6 = (3x3 + -2x3 + x4)(-5x2) + (x + 3x3 + -2x3)(x)

Combine like terms: 3x3 + -2x3 = 1x3
1x4 + -4x5 + -5x6 = (1x3 + x4)(-5x2) + (x + 3x3 + -2x3)(x)

Remove parenthesis around (-5x2)
1x4 + -4x5 + -5x6 = (1x3 + x4) * -5x2 + (x + 3x3 + -2x3)(x)

Reorder the terms for easier multiplication:
1x4 + -4x5 + -5x6 = -5x2(1x3 + x4) + (x + 3x3 + -2x3)(x)
1x4 + -4x5 + -5x6 = (1x3 * -5x2 + x4 * -5x2) + (x + 3x3 + -2x3)(x)
1x4 + -4x5 + -5x6 = (-5x5 + -5x6) + (x + 3x3 + -2x3)(x)

Combine like terms: 3x3 + -2x3 = 1x3
1x4 + -4x5 + -5x6 = -5x5 + -5x6 + (x + 1x3)(x)

Reorder the terms for easier multiplication:
1x4 + -4x5 + -5x6 = -5x5 + -5x6 + x(x + 1x3)
1x4 + -4x5 + -5x6 = -5x5 + -5x6 + (x * x + 1x3 * x)
1x4 + -4x5 + -5x6 = -5x5 + -5x6 + (x2 + 1x4)

Reorder the terms:
1x4 + -4x5 + -5x6 = x2 + 1x4 + -5x5 + -5x6

Add '-1x4' to each side of the equation.
1x4 + -4x5 + -1x4 + -5x6 = x2 + 1x4 + -5x5 + -1x4 + -5x6

Reorder the terms:
1x4 + -1x4 + -4x5 + -5x6 = x2 + 1x4 + -5x5 + -1x4 + -5x6

Combine like terms: 1x4 + -1x4 = 0
0 + -4x5 + -5x6 = x2 + 1x4 + -5x5 + -1x4 + -5x6
-4x5 + -5x6 = x2 + 1x4 + -5x5 + -1x4 + -5x6

Reorder the terms:
-4x5 + -5x6 = x2 + 1x4 + -1x4 + -5x5 + -5x6

Combine like terms: 1x4 + -1x4 = 0
-4x5 + -5x6 = x2 + 0 + -5x5 + -5x6
-4x5 + -5x6 = x2 + -5x5 + -5x6

Add '5x6' to each side of the equation.
-4x5 + -5x6 + 5x6 = x2 + -5x5 + -5x6 + 5x6

Combine like terms: -5x6 + 5x6 = 0
-4x5 + 0 = x2 + -5x5 + -5x6 + 5x6
-4x5 = x2 + -5x5 + -5x6 + 5x6

Combine like terms: -5x6 + 5x6 = 0
-4x5 = x2 + -5x5 + 0
-4x5 = x2 + -5x5

Solving
-4x5 = x2 + -5x5

Solving for variable 'x'.

Reorder the terms:
-1x2 + -4x5 + 5x5 = x2 + -5x5 + -1x2 + 5x5

Combine like terms: -4x5 + 5x5 = 1x5
-1x2 + 1x5 = x2 + -5x5 + -1x2 + 5x5

Reorder the terms:
-1x2 + 1x5 = x2 + -1x2 + -5x5 + 5x5

Combine like terms: x2 + -1x2 = 0
-1x2 + 1x5 = 0 + -5x5 + 5x5
-1x2 + 1x5 = -5x5 + 5x5

Combine like terms: -5x5 + 5x5 = 0
-1x2 + 1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + x3) = 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 '(-1 + x3)' equal to zero and attempt to solve:

Simplifying
-1 + x3 = 0

Solving
-1 + x3 = 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 + x3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x3 = 0 + 1
x3 = 0 + 1

Combine like terms: 0 + 1 = 1
x3 = 1

Simplifying
x3 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}