0=4x^3+3x^2-10x

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Solution for 0=4x^3+3x^2-10x equation: 


Simplifying
0 = 4x3 + 3x2 + -10x

Reorder the terms:
0 = -10x + 3x2 + 4x3

Solving
0 = -10x + 3x2 + 4x3

Solving for variable 'x'.
Remove the zero:
10x + -3x2 + -4x3 = -10x + 3x2 + 4x3 + 10x + -3x2 + -4x3

Reorder the terms:
10x + -3x2 + -4x3 = -10x + 10x + 3x2 + -3x2 + 4x3 + -4x3

Combine like terms: -10x + 10x = 0
10x + -3x2 + -4x3 = 0 + 3x2 + -3x2 + 4x3 + -4x3
10x + -3x2 + -4x3 = 3x2 + -3x2 + 4x3 + -4x3

Combine like terms: 3x2 + -3x2 = 0
10x + -3x2 + -4x3 = 0 + 4x3 + -4x3
10x + -3x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
10x + -3x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -3x + -4x2) = 0

Factor a trinomial.
x((5 + -4x)(2 + x)) = 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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {0, 1.25, -2}

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