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

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


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

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

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

Multiply (8 + 3x) * (-3 + 2x)
(8(-3 + 2x) + 3x * (-3 + 2x)) = 0
((-3 * 8 + 2x * 8) + 3x * (-3 + 2x)) = 0
((-24 + 16x) + 3x * (-3 + 2x)) = 0
(-24 + 16x + (-3 * 3x + 2x * 3x)) = 0
(-24 + 16x + (-9x + 6x2)) = 0

Combine like terms: 16x + -9x = 7x
(-24 + 7x + 6x2) = 0

Solving
-24 + 7x + 6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2.666666667, 1.5}

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