x(2x-1)=36

Solution for x(2x-1)=36 equation:

Simplifying
x(2x + -1) = 36

Reorder the terms:
x(-1 + 2x) = 36
(-1 * x + 2x * x) = 36
(-1x + 2x2) = 36

Solving
-1x + 2x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + -1x + 2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -1x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(9 + -2x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 4.5}