(4x+1)(x+1)=52

Solution for (4x+1)(x+1)=52 equation:

Simplifying
(4x + 1)(x + 1) = 52

Reorder the terms:
(1 + 4x)(x + 1) = 52

Reorder the terms:
(1 + 4x)(1 + x) = 52

Multiply (1 + 4x) * (1 + x)
(1(1 + x) + 4x * (1 + x)) = 52
((1 * 1 + x * 1) + 4x * (1 + x)) = 52
((1 + 1x) + 4x * (1 + x)) = 52
(1 + 1x + (1 * 4x + x * 4x)) = 52
(1 + 1x + (4x + 4x2)) = 52

Combine like terms: 1x + 4x = 5x
(1 + 5x + 4x2) = 52

Solving
1 + 5x + 4x2 = 52

Solving for variable 'x'.

Reorder the terms:
1 + -52 + 5x + 4x2 = 52 + -52

Combine like terms: 1 + -52 = -51
-51 + 5x + 4x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-51 + 5x + 4x2 = 0

Factor a trinomial.
(-17 + -4x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -4x)' equal to zero and attempt to solve:

Simplifying
-17 + -4x = 0

Solving
-17 + -4x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -4x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -4x = 0 + 17
-4x = 0 + 17

Combine like terms: 0 + 17 = 17
-4x = 17

Divide each side by '-4'.
x = -4.25

Simplifying
x = -4.25
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 = {-4.25, 3}