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

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


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

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

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

Multiply (-4 + 3x) * (2 + x)
(-4(2 + x) + 3x * (2 + x)) = 48
((2 * -4 + x * -4) + 3x * (2 + x)) = 48
((-8 + -4x) + 3x * (2 + x)) = 48
(-8 + -4x + (2 * 3x + x * 3x)) = 48
(-8 + -4x + (6x + 3x2)) = 48

Combine like terms: -4x + 6x = 2x
(-8 + 2x + 3x2) = 48

Solving
-8 + 2x + 3x2 = 48

Solving for variable 'x'.

Reorder the terms:
-8 + -48 + 2x + 3x2 = 48 + -48

Combine like terms: -8 + -48 = -56
-56 + 2x + 3x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-56 + 2x + 3x2 = 0

Factor a trinomial.
(-14 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-14 + -3x)' equal to zero and attempt to solve:

Simplifying
-14 + -3x = 0

Solving
-14 + -3x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -3x = 0 + 14

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

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

Divide each side by '-3'.
x = -4.666666667

Simplifying
x = -4.666666667

Subproblem 2
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
Solution
x = {-4.666666667, 4}

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