x(x-10)(2x+1)=0

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Solution for x(x-10)(2x+1)=0 equation: 


Simplifying
x(x + -10)(2x + 1) = 0

Reorder the terms:
x(-10 + x)(2x + 1) = 0

Reorder the terms:
x(-10 + x)(1 + 2x) = 0

Multiply (-10 + x) * (1 + 2x)
x(-10(1 + 2x) + x(1 + 2x)) = 0
x((1 * -10 + 2x * -10) + x(1 + 2x)) = 0
x((-10 + -20x) + x(1 + 2x)) = 0
x(-10 + -20x + (1 * x + 2x * x)) = 0
x(-10 + -20x + (1x + 2x2)) = 0

Combine like terms: -20x + 1x = -19x
x(-10 + -19x + 2x2) = 0
(-10 * x + -19x * x + 2x2 * x) = 0
(-10x + -19x2 + 2x3) = 0

Solving
-10x + -19x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + -19x + 2x2) = 0

Factor a trinomial.
x((-1 + -2x)(10 + -1x)) = 0


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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, -0.5, 10}

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