(3x+2)(8-4x)=0

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Solution for (3x+2)(8-4x)=0 equation: 


Simplifying
(3x + 2)(8 + -4x) = 0

Reorder the terms:
(2 + 3x)(8 + -4x) = 0

Multiply (2 + 3x) * (8 + -4x)
(2(8 + -4x) + 3x * (8 + -4x)) = 0
((8 * 2 + -4x * 2) + 3x * (8 + -4x)) = 0
((16 + -8x) + 3x * (8 + -4x)) = 0
(16 + -8x + (8 * 3x + -4x * 3x)) = 0
(16 + -8x + (24x + -12x2)) = 0

Combine like terms: -8x + 24x = 16x
(16 + 16x + -12x2) = 0

Solving
16 + 16x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 4x + -3x2) = 0

Factor a trinomial.
4((2 + -1x)(2 + 3x)) = 0

Ignore the factor 4.

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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {2, -0.6666666667}

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