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

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


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

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

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

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

Combine like terms: -15x + 8x = -7x
(-40 + -7x + 3x2) = 0

Solving
-40 + -7x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2.666666667, 5}

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