3x(x-1)=2(x^2+27)

Solution for 3x(x-1)=2(x^2+27) equation:

Simplifying
3x(x + -1) = 2(x2 + 27)

Reorder the terms:
3x(-1 + x) = 2(x2 + 27)
(-1 * 3x + x * 3x) = 2(x2 + 27)
(-3x + 3x2) = 2(x2 + 27)

Reorder the terms:
-3x + 3x2 = 2(27 + x2)
-3x + 3x2 = (27 * 2 + x2 * 2)
-3x + 3x2 = (54 + 2x2)

Solving
-3x + 3x2 = 54 + 2x2

Solving for variable 'x'.

Reorder the terms:
-54 + -3x + 3x2 + -2x2 = 54 + 2x2 + -54 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-54 + -3x + 1x2 = 54 + 2x2 + -54 + -2x2

Reorder the terms:
-54 + -3x + 1x2 = 54 + -54 + 2x2 + -2x2

Combine like terms: 54 + -54 = 0
-54 + -3x + 1x2 = 0 + 2x2 + -2x2
-54 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-54 + -3x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-6, 9}