(4x+1)(x+1)=7

Solution for (4x+1)(x+1)=7 equation:

Simplifying
(4x + 1)(x + 1) = 7

Reorder the terms:
(1 + 4x)(x + 1) = 7

Reorder the terms:
(1 + 4x)(1 + x) = 7

Multiply (1 + 4x) * (1 + x)
(1(1 + x) + 4x * (1 + x)) = 7
((1 * 1 + x * 1) + 4x * (1 + x)) = 7
((1 + 1x) + 4x * (1 + x)) = 7
(1 + 1x + (1 * 4x + x * 4x)) = 7
(1 + 1x + (4x + 4x2)) = 7

Combine like terms: 1x + 4x = 5x
(1 + 5x + 4x2) = 7

Solving
1 + 5x + 4x2 = 7

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 5x + 4x2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 5x + 4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + 5x + 4x2 = 0

Factor a trinomial.
(-2 + -1x)(3 + -4x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-2, 0.75}