2x(28x^2-8x-3)=0

Solution for 2x(28x^2-8x-3)=0 equation:

Simplifying
2x(28x2 + -8x + -3) = 0

Reorder the terms:
2x(-3 + -8x + 28x2) = 0
(-3 * 2x + -8x * 2x + 28x2 * 2x) = 0
(-6x + -16x2 + 56x3) = 0

Solving
-6x + -16x2 + 56x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + -8x + 28x2) = 0

Factor a trinomial.
2x((-3 + -14x)(1 + -2x)) = 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 '(-3 + -14x)' equal to zero and attempt to solve:

Simplifying
-3 + -14x = 0

Solving
-3 + -14x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -14x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -14x = 0 + 3
-14x = 0 + 3

Combine like terms: 0 + 3 = 3
-14x = 3

Divide each side by '-14'.
x = -0.2142857143

Simplifying
x = -0.2142857143
Subproblem 3
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
Solution
x = {0, -0.2142857143, 0.5}