48=(x+2)(x+4)

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Solution for 48=(x+2)(x+4) equation: 


Simplifying
48 = (x + 2)(x + 4)

Reorder the terms:
48 = (2 + x)(x + 4)

Reorder the terms:
48 = (2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
48 = (2(4 + x) + x(4 + x))
48 = ((4 * 2 + x * 2) + x(4 + x))
48 = ((8 + 2x) + x(4 + x))
48 = (8 + 2x + (4 * x + x * x))
48 = (8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
48 = (8 + 6x + x2)

Solving
48 = 8 + 6x + x2

Solving for variable 'x'.

Combine like terms: 48 + -8 = 40
40 + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
40 + -6x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
40 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
40 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
40 + -6x + -1x2 = 0 + x2 + -1x2
40 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + -6x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(10 + x) = 0


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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {4, -10}

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