(3x-8)(2x+1)=0

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Solution for (3x-8)(2x+1)=0 equation: 


Simplifying
(3x + -8)(2x + 1) = 0

Reorder the terms:
(-8 + 3x)(2x + 1) = 0

Reorder the terms:
(-8 + 3x)(1 + 2x) = 0

Multiply (-8 + 3x) * (1 + 2x)
(-8(1 + 2x) + 3x * (1 + 2x)) = 0
((1 * -8 + 2x * -8) + 3x * (1 + 2x)) = 0
((-8 + -16x) + 3x * (1 + 2x)) = 0
(-8 + -16x + (1 * 3x + 2x * 3x)) = 0
(-8 + -16x + (3x + 6x2)) = 0

Combine like terms: -16x + 3x = -13x
(-8 + -13x + 6x2) = 0

Solving
-8 + -13x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x)(8 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-0.5, 2.666666667}

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