x(2x-1)=21

Solution for x(2x-1)=21 equation:

Simplifying
x(2x + -1) = 21

Reorder the terms:
x(-1 + 2x) = 21
(-1 * x + 2x * x) = 21
(-1x + 2x2) = 21

Solving
-1x + 2x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -1x + 2x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -1x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -2x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-3, 3.5}