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

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


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

Reorder the terms:
(3 + 6x)(3x) = 0

Remove parenthesis around (3x)
(3 + 6x) * 3x = 0

Reorder the terms for easier multiplication:
3x(3 + 6x) = 0
(3 * 3x + 6x * 3x) = 0
(9x + 18x2) = 0

Solving
9x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(1 + 2x) = 0

Ignore the factor 9.

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}

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