(4x+1)*(x+1)=126

Solution for (4x+1)*(x+1)=126 equation:

Simplifying
(4x + 1)(x + 1) = 126

Reorder the terms:
(1 + 4x)(x + 1) = 126

Reorder the terms:
(1 + 4x)(1 + x) = 126

Multiply (1 + 4x) * (1 + x)
(1(1 + x) + 4x * (1 + x)) = 126
((1 * 1 + x * 1) + 4x * (1 + x)) = 126
((1 + 1x) + 4x * (1 + x)) = 126
(1 + 1x + (1 * 4x + x * 4x)) = 126
(1 + 1x + (4x + 4x2)) = 126

Combine like terms: 1x + 4x = 5x
(1 + 5x + 4x2) = 126

Solving
1 + 5x + 4x2 = 126

Solving for variable 'x'.

Reorder the terms:
1 + -126 + 5x + 4x2 = 126 + -126

Combine like terms: 1 + -126 = -125
-125 + 5x + 4x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-125 + 5x + 4x2 = 0

Factor a trinomial.
(-25 + -4x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-25 + -4x)' equal to zero and attempt to solve:

Simplifying
-25 + -4x = 0

Solving
-25 + -4x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -4x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4x = 0 + 25
-4x = 0 + 25

Combine like terms: 0 + 25 = 25
-4x = 25

Divide each side by '-4'.
x = -6.25

Simplifying
x = -6.25
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6.25, 5}