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

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


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

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

Reorder the terms:
1x + x2 = 3x(-3 + 2x)
1x + x2 = (-3 * 3x + 2x * 3x)
1x + x2 = (-9x + 6x2)

Solving
1x + x2 = -9x + 6x2

Solving for variable 'x'.

Reorder the terms:
1x + 9x + x2 + -6x2 = -9x + 6x2 + 9x + -6x2

Combine like terms: 1x + 9x = 10x
10x + x2 + -6x2 = -9x + 6x2 + 9x + -6x2

Combine like terms: x2 + -6x2 = -5x2
10x + -5x2 = -9x + 6x2 + 9x + -6x2

Reorder the terms:
10x + -5x2 = -9x + 9x + 6x2 + -6x2

Combine like terms: -9x + 9x = 0
10x + -5x2 = 0 + 6x2 + -6x2
10x + -5x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + -1x) = 0

Ignore the factor 5.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}

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