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

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


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

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

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

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

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

Solving
8 + 14x + 3x2 = 48

Solving for variable 'x'.

Reorder the terms:
8 + -48 + 14x + 3x2 = 48 + -48

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

Combine like terms: 48 + -48 = 0
-40 + 14x + 3x2 = 0

Factor a trinomial.
(-20 + -3x)(2 + -1x) = 0


Subproblem 1
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

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 = {-6.666666667, 2}

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