(8x^3-4x^2+x)-(2x^3+9x^2-4x)=

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Solution for (8x^3-4x^2+x)-(2x^3+9x^2-4x)= equation: 


Simplifying
(8x3 + -4x2 + x) + -1(2x3 + 9x2 + -4x) = 0

Reorder the terms:
(x + -4x2 + 8x3) + -1(2x3 + 9x2 + -4x) = 0

Remove parenthesis around (x + -4x2 + 8x3)
x + -4x2 + 8x3 + -1(2x3 + 9x2 + -4x) = 0

Reorder the terms:
x + -4x2 + 8x3 + -1(-4x + 9x2 + 2x3) = 0
x + -4x2 + 8x3 + (-4x * -1 + 9x2 * -1 + 2x3 * -1) = 0
x + -4x2 + 8x3 + (4x + -9x2 + -2x3) = 0

Reorder the terms:
x + 4x + -4x2 + -9x2 + 8x3 + -2x3 = 0

Combine like terms: x + 4x = 5x
5x + -4x2 + -9x2 + 8x3 + -2x3 = 0

Combine like terms: -4x2 + -9x2 = -13x2
5x + -13x2 + 8x3 + -2x3 = 0

Combine like terms: 8x3 + -2x3 = 6x3
5x + -13x2 + 6x3 = 0

Solving
5x + -13x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -13x + 6x2) = 0

Factor a trinomial.
x((1 + -2x)(5 + -3x)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 0.5, 1.666666667}

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