(2x+1)*2x=20

Solution for (2x+1)*2x=20 equation:

Simplifying
(2x + 1) * 2x = 20

Reorder the terms:
(1 + 2x) * 2x = 20

Reorder the terms for easier multiplication:
2x(1 + 2x) = 20
(1 * 2x + 2x * 2x) = 20
(2x + 4x2) = 20

Solving
2x + 4x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 2x + 4x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + x + 2x2) = 0

Factor a trinomial.
2((-5 + -2x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.5, 2}