6x(6x)+3x=0

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


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

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

Reorder the terms for easier multiplication:
6 * 6x * x + 3x = 0

Multiply 6 * 6
36x * x + 3x = 0

Multiply x * x
36x2 + 3x = 0

Reorder the terms:
3x + 36x2 = 0

Solving
3x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 12x) = 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 '(1 + 12x)' equal to zero and attempt to solve:

Simplifying
1 + 12x = 0

Solving
1 + 12x = 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 + 12x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12x = 0 + -1
12x = 0 + -1

Combine like terms: 0 + -1 = -1
12x = -1

Divide each side by '12'.
x = -0.08333333333

Simplifying
x = -0.08333333333
Solution
x = {0, -0.08333333333}

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