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

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


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

Reorder the terms:
3x(-2 + x) = x(x + 1)
(-2 * 3x + x * 3x) = x(x + 1)
(-6x + 3x2) = x(x + 1)

Reorder the terms:
-6x + 3x2 = x(1 + x)
-6x + 3x2 = (1 * x + x * x)
-6x + 3x2 = (1x + x2)

Solving
-6x + 3x2 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
-6x + -1x + 3x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: -6x + -1x = -7x
-7x + 3x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-7x + 2x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-7x + 2x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-7x + 2x2 = 0 + x2 + -1x2
-7x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 2x) = 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 '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 3.5}

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