2x(x+1)+x(x-2)-3x(3x-1)=

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


Simplifying
2x(x + 1) + x(x + -2) + -3x(3x + -1) = 0

Reorder the terms:
2x(1 + x) + x(x + -2) + -3x(3x + -1) = 0
(1 * 2x + x * 2x) + x(x + -2) + -3x(3x + -1) = 0
(2x + 2x2) + x(x + -2) + -3x(3x + -1) = 0

Reorder the terms:
2x + 2x2 + x(-2 + x) + -3x(3x + -1) = 0
2x + 2x2 + (-2 * x + x * x) + -3x(3x + -1) = 0
2x + 2x2 + (-2x + x2) + -3x(3x + -1) = 0

Reorder the terms:
2x + 2x2 + -2x + x2 + -3x(-1 + 3x) = 0
2x + 2x2 + -2x + x2 + (-1 * -3x + 3x * -3x) = 0
2x + 2x2 + -2x + x2 + (3x + -9x2) = 0

Reorder the terms:
2x + -2x + 3x + 2x2 + x2 + -9x2 = 0

Combine like terms: 2x + -2x = 0
0 + 3x + 2x2 + x2 + -9x2 = 0
3x + 2x2 + x2 + -9x2 = 0

Combine like terms: 2x2 + x2 = 3x2
3x + 3x2 + -9x2 = 0

Combine like terms: 3x2 + -9x2 = -6x2
3x + -6x2 = 0

Solving
3x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + -2x) = 0

Ignore the factor 3.

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
Solution
x = {0, 0.5}

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