(x+1)(4x)=48

Solution for (x+1)(4x)=48 equation:

Simplifying
(x + 1)(4x) = 48

Reorder the terms:
(1 + x)(4x) = 48

Remove parenthesis around (4x)
(1 + x) * 4x = 48

Reorder the terms for easier multiplication:
4x(1 + x) = 48
(1 * 4x + x * 4x) = 48
(4x + 4x2) = 48

Solving
4x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 4x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + x + x2) = 0

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

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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, 3}