3x(2x-3)=6x

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Solution for 3x(2x-3)=6x equation: 


Simplifying
3x(2x + -3) = 6x

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

Solving
-9x + 6x2 = 6x

Solving for variable 'x'.

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

Combine like terms: -9x + -6x = -15x
-15x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + 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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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