(2x^3+5x^2)(1-2x)=0

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Solution for (2x^3+5x^2)(1-2x)=0 equation: 


Simplifying
(2x3 + 5x2)(1 + -2x) = 0

Reorder the terms:
(5x2 + 2x3)(1 + -2x) = 0

Multiply (5x2 + 2x3) * (1 + -2x)
(5x2 * (1 + -2x) + 2x3 * (1 + -2x)) = 0
((1 * 5x2 + -2x * 5x2) + 2x3 * (1 + -2x)) = 0
((5x2 + -10x3) + 2x3 * (1 + -2x)) = 0
(5x2 + -10x3 + (1 * 2x3 + -2x * 2x3)) = 0
(5x2 + -10x3 + (2x3 + -4x4)) = 0

Combine like terms: -10x3 + 2x3 = -8x3
(5x2 + -8x3 + -4x4) = 0

Solving
5x2 + -8x3 + -4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(5 + -8x + -4x2) = 0

Factor a trinomial.
x2((1 + -2x)(5 + 2x)) = 0


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 '(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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, 0.5, -2.5}

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