2x(x+5)x=50x-2x^3

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Solution for 2x(x+5)x=50x-2x^3 equation: 


Simplifying
2x(x + 5) * x = 50x + -2x3

Reorder the terms:
2x(5 + x) * x = 50x + -2x3

Reorder the terms for easier multiplication:
2x * x(5 + x) = 50x + -2x3

Multiply x * x
2x2(5 + x) = 50x + -2x3
(5 * 2x2 + x * 2x2) = 50x + -2x3
(10x2 + 2x3) = 50x + -2x3

Solving
10x2 + 2x3 = 50x + -2x3

Solving for variable 'x'.

Reorder the terms:
-50x + 10x2 + 2x3 + 2x3 = 50x + -2x3 + -50x + 2x3

Combine like terms: 2x3 + 2x3 = 4x3
-50x + 10x2 + 4x3 = 50x + -2x3 + -50x + 2x3

Reorder the terms:
-50x + 10x2 + 4x3 = 50x + -50x + -2x3 + 2x3

Combine like terms: 50x + -50x = 0
-50x + 10x2 + 4x3 = 0 + -2x3 + 2x3
-50x + 10x2 + 4x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
-50x + 10x2 + 4x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-25 + 5x + 2x2) = 0

Factor a trinomial.
2x((-5 + -1x)(5 + -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 '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -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, -5, 2.5}

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