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

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


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

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

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

Combine like terms: 1 + -4 = -3
x(-3 + x + 2x + -1x + x2) = 0

Combine like terms: x + 2x = 3x
x(-3 + 3x + -1x + x2) = 0

Combine like terms: 3x + -1x = 2x
x(-3 + 2x + x2) = 0
(-3 * x + 2x * x + x2 * x) = 0
(-3x + 2x2 + x3) = 0

Solving
-3x + 2x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 2x + x2) = 0

Factor a trinomial.
x((-3 + -1x)(1 + -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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, -3, 1}

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