48=(3x+2)(x+4)

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Solution for 48=(3x+2)(x+4) equation: 


Simplifying
48 = (3x + 2)(x + 4)

Reorder the terms:
48 = (2 + 3x)(x + 4)

Reorder the terms:
48 = (2 + 3x)(4 + x)

Multiply (2 + 3x) * (4 + x)
48 = (2(4 + x) + 3x * (4 + x))
48 = ((4 * 2 + x * 2) + 3x * (4 + x))
48 = ((8 + 2x) + 3x * (4 + x))
48 = (8 + 2x + (4 * 3x + x * 3x))
48 = (8 + 2x + (12x + 3x2))

Combine like terms: 2x + 12x = 14x
48 = (8 + 14x + 3x2)

Solving
48 = 8 + 14x + 3x2

Solving for variable 'x'.

Combine like terms: 48 + -8 = 40
40 + -14x + -3x2 = 8 + 14x + 3x2 + -8 + -14x + -3x2

Reorder the terms:
40 + -14x + -3x2 = 8 + -8 + 14x + -14x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
40 + -14x + -3x2 = 0 + 14x + -14x + 3x2 + -3x2
40 + -14x + -3x2 = 14x + -14x + 3x2 + -3x2

Combine like terms: 14x + -14x = 0
40 + -14x + -3x2 = 0 + 3x2 + -3x2
40 + -14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
40 + -14x + -3x2 = 0

Factor a trinomial.
(2 + -1x)(20 + 3x) = 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 '(20 + 3x)' equal to zero and attempt to solve:

Simplifying
20 + 3x = 0

Solving
20 + 3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + 3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 3x = 0 + -20
3x = 0 + -20

Combine like terms: 0 + -20 = -20
3x = -20

Divide each side by '3'.
x = -6.666666667

Simplifying
x = -6.666666667
Solution
x = {2, -6.666666667}

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