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

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


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

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

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

Multiply (-8 + 3x) * (3 + 8x)
(-8(3 + 8x) + 3x * (3 + 8x)) = 0
((3 * -8 + 8x * -8) + 3x * (3 + 8x)) = 0
((-24 + -64x) + 3x * (3 + 8x)) = 0
(-24 + -64x + (3 * 3x + 8x * 3x)) = 0
(-24 + -64x + (9x + 24x2)) = 0

Combine like terms: -64x + 9x = -55x
(-24 + -55x + 24x2) = 0

Solving
-24 + -55x + 24x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve:

Simplifying
-3 + -8x = 0

Solving
-3 + -8x = 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 + -8x = 0 + 3

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

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

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375

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 = {-0.375, 2.666666667}

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