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

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


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

Reorder the terms:
3x(8 + x) + 5(x + 8) = 0
(8 * 3x + x * 3x) + 5(x + 8) = 0
(24x + 3x2) + 5(x + 8) = 0

Reorder the terms:
24x + 3x2 + 5(8 + x) = 0
24x + 3x2 + (8 * 5 + x * 5) = 0
24x + 3x2 + (40 + 5x) = 0

Reorder the terms:
40 + 24x + 5x + 3x2 = 0

Combine like terms: 24x + 5x = 29x
40 + 29x + 3x2 = 0

Solving
40 + 29x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-8, -1.666666667}

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