(x+6)(x+4)=48

Solution for (x+6)(x+4)=48 equation:

Simplifying
(x + 6)(x + 4) = 48

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

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

Multiply (6 + x) * (4 + x)
(6(4 + x) + x(4 + x)) = 48
((4 * 6 + x * 6) + x(4 + x)) = 48
((24 + 6x) + x(4 + x)) = 48
(24 + 6x + (4 * x + x * x)) = 48
(24 + 6x + (4x + x2)) = 48

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = 48

Solving
24 + 10x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
24 + -48 + 10x + x2 = 48 + -48

Combine like terms: 24 + -48 = -24
-24 + 10x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-24 + 10x + x2 = 0

Factor a trinomial.
(-12 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 2}