2x^2(x-4)(-2x+1)=0

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Solution for 2x^2(x-4)(-2x+1)=0 equation: 


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

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

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

Multiply (-4 + x) * (1 + -2x)
2x2(-4(1 + -2x) + x(1 + -2x)) = 0
2x2((1 * -4 + -2x * -4) + x(1 + -2x)) = 0
2x2((-4 + 8x) + x(1 + -2x)) = 0
2x2(-4 + 8x + (1 * x + -2x * x)) = 0
2x2(-4 + 8x + (1x + -2x2)) = 0

Combine like terms: 8x + 1x = 9x
2x2(-4 + 9x + -2x2) = 0
(-4 * 2x2 + 9x * 2x2 + -2x2 * 2x2) = 0
(-8x2 + 18x3 + -4x4) = 0

Solving
-8x2 + 18x3 + -4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-4 + 9x + -2x2) = 0

Factor a trinomial.
2x2((-4 + x)(1 + -2x)) = 0

Ignore the factor 2.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4

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, 4, 0.5}

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