2x(2x+1)=42

Solution for 2x(2x+1)=42 equation:

Simplifying
2x(2x + 1) = 42

Reorder the terms:
2x(1 + 2x) = 42
(1 * 2x + 2x * 2x) = 42
(2x + 4x2) = 42

Solving
2x + 4x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 2x + 4x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + x + 2x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-3.5, 3}