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

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


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

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

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

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

Combine like terms: -5x + 24x = 19x
0 = (-40 + 19x + 3x2)

Solving
0 = -40 + 19x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 40 = 40
40 + -19x + -3x2 = -40 + 19x + 3x2 + 40 + -19x + -3x2

Reorder the terms:
40 + -19x + -3x2 = -40 + 40 + 19x + -19x + 3x2 + -3x2

Combine like terms: -40 + 40 = 0
40 + -19x + -3x2 = 0 + 19x + -19x + 3x2 + -3x2
40 + -19x + -3x2 = 19x + -19x + 3x2 + -3x2

Combine like terms: 19x + -19x = 0
40 + -19x + -3x2 = 0 + 3x2 + -3x2
40 + -19x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
40 + -19x + -3x2 = 0

Factor a trinomial.
(5 + -3x)(8 + x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

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

Simplifying
8 + x = 0

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

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

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

Simplifying
x = -8
Solution
x = {1.666666667, -8}

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