(2x+1)(x+3)=42

Solution for (2x+1)(x+3)=42 equation:

Simplifying
(2x + 1)(x + 3) = 42

Reorder the terms:
(1 + 2x)(x + 3) = 42

Reorder the terms:
(1 + 2x)(3 + x) = 42

Multiply (1 + 2x) * (3 + x)
(1(3 + x) + 2x * (3 + x)) = 42
((3 * 1 + x * 1) + 2x * (3 + x)) = 42
((3 + 1x) + 2x * (3 + x)) = 42
(3 + 1x + (3 * 2x + x * 2x)) = 42
(3 + 1x + (6x + 2x2)) = 42

Combine like terms: 1x + 6x = 7x
(3 + 7x + 2x2) = 42

Solving
3 + 7x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
3 + -42 + 7x + 2x2 = 42 + -42

Combine like terms: 3 + -42 = -39
-39 + 7x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-39 + 7x + 2x2 = 0

Factor a trinomial.
(-13 + -2x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
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 = {-6.5, 3}