6x(3x-5)+12x=0

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Solution for 6x(3x-5)+12x=0 equation: 


Simplifying
6x(3x + -5) + 12x = 0

Reorder the terms:
6x(-5 + 3x) + 12x = 0
(-5 * 6x + 3x * 6x) + 12x = 0
(-30x + 18x2) + 12x = 0

Reorder the terms:
-30x + 12x + 18x2 = 0

Combine like terms: -30x + 12x = -18x
-18x + 18x2 = 0

Solving
-18x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18x'.
18x(-1 + x) = 0

Ignore the factor 18.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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