(4x^3)-8x=14x^2

Solution for (4x^3)-8x=14x^2 equation:

Simplifying
(4x3) + -8x = 14x2

Reorder the terms:
-8x + (4x3) = 14x2

Solving
-8x + (4x3) = 14x2

Solving for variable 'x'.

Reorder the terms:
-8x + -14x2 + (4x3) = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-8x + -14x2 + (4x3) = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + -7x + (2x2)) = 0

Factor a trinomial.
2x((-1 + -2x)(4 + -1x)) = 0

Ignore the factor 2.
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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -0.5, 4}