9x(2x-3)=81x

Solution for 9x(2x-3)=81x equation:

Simplifying
9x(2x + -3) = 81x

Reorder the terms:
9x(-3 + 2x) = 81x
(-3 * 9x + 2x * 9x) = 81x
(-27x + 18x2) = 81x

Solving
-27x + 18x2 = 81x

Solving for variable 'x'.

Reorder the terms:
-27x + -81x + 18x2 = 81x + -81x

Combine like terms: -27x + -81x = -108x
-108x + 18x2 = 81x + -81x

Combine like terms: 81x + -81x = 0
-108x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '18x'.
18x(-6 + 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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}