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

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


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

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

Solving
3x + 3x2 = 9x + -3x2

Solving for variable 'x'.

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

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

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

Reorder the terms:
-6x + 6x2 = 9x + -9x + -3x2 + 3x2

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

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

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-1 + x) = 0

Ignore the factor 6.

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

Simplifying
-1 + x = 0

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

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

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

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

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