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

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


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

Reorder the terms:
5x(3 + x) + -8(x + 3) = 0
(3 * 5x + x * 5x) + -8(x + 3) = 0
(15x + 5x2) + -8(x + 3) = 0

Reorder the terms:
15x + 5x2 + -8(3 + x) = 0
15x + 5x2 + (3 * -8 + x * -8) = 0
15x + 5x2 + (-24 + -8x) = 0

Reorder the terms:
-24 + 15x + -8x + 5x2 = 0

Combine like terms: 15x + -8x = 7x
-24 + 7x + 5x2 = 0

Solving
-24 + 7x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(8 + -5x) = 0


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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-3, 1.6}

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