(5x-3)(3x+8)=0

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Solution for (5x-3)(3x+8)=0 equation: 


Simplifying
(5x + -3)(3x + 8) = 0

Reorder the terms:
(-3 + 5x)(3x + 8) = 0

Reorder the terms:
(-3 + 5x)(8 + 3x) = 0

Multiply (-3 + 5x) * (8 + 3x)
(-3(8 + 3x) + 5x * (8 + 3x)) = 0
((8 * -3 + 3x * -3) + 5x * (8 + 3x)) = 0
((-24 + -9x) + 5x * (8 + 3x)) = 0
(-24 + -9x + (8 * 5x + 3x * 5x)) = 0
(-24 + -9x + (40x + 15x2)) = 0

Combine like terms: -9x + 40x = 31x
(-24 + 31x + 15x2) = 0

Solving
-24 + 31x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(3 + -5x) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-2.666666667, 0.6}

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