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

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

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

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

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

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

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

Solving
52 = 1 + 5x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
51 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
51 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
51 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

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

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

Factor a trinomial.
(3 + -1x)(17 + 4x) = 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 '(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
Solution
x = {3, -4.25}