2x(x-6)+3x=0

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Solution for 2x(x-6)+3x=0 equation: 


Simplifying
2x(x + -6) + 3x = 0

Reorder the terms:
2x(-6 + x) + 3x = 0
(-6 * 2x + x * 2x) + 3x = 0
(-12x + 2x2) + 3x = 0

Reorder the terms:
-12x + 3x + 2x2 = 0

Combine like terms: -12x + 3x = -9x
-9x + 2x2 = 0

Solving
-9x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + 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 '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying
-9 + 2x = 0

Solving
-9 + 2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9

Combine like terms: 0 + 9 = 9
2x = 9

Divide each side by '2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {0, 4.5}

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