6x(x-1)=21x

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Solution for 6x(x-1)=21x equation: 


Simplifying
6x(x + -1) = 21x

Reorder the terms:
6x(-1 + x) = 21x
(-1 * 6x + x * 6x) = 21x
(-6x + 6x2) = 21x

Solving
-6x + 6x2 = 21x

Solving for variable 'x'.

Reorder the terms:
-6x + -21x + 6x2 = 21x + -21x

Combine like terms: -6x + -21x = -27x
-27x + 6x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-27x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + 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 '(-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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