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

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


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

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

Reorder the terms:
-15x + 3x2 + 8(-5 + x) = 0
-15x + 3x2 + (-5 * 8 + x * 8) = 0
-15x + 3x2 + (-40 + 8x) = 0

Reorder the terms:
-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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