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

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


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

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

Reorder the terms:
-15x + 3x2 + 5(-5 + x) = 0
-15x + 3x2 + (-5 * 5 + x * 5) = 0
-15x + 3x2 + (-25 + 5x) = 0

Reorder the terms:
-25 + -15x + 5x + 3x2 = 0

Combine like terms: -15x + 5x = -10x
-25 + -10x + 3x2 = 0

Solving
-25 + -10x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(5 + -1x) = 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 '(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 = {-1.666666667, 5}

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