5x(x+1)=6x(x-5)

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Solution for 5x(x+1)=6x(x-5) equation: 


Simplifying
5x(x + 1) = 6x(x + -5)

Reorder the terms:
5x(1 + x) = 6x(x + -5)
(1 * 5x + x * 5x) = 6x(x + -5)
(5x + 5x2) = 6x(x + -5)

Reorder the terms:
5x + 5x2 = 6x(-5 + x)
5x + 5x2 = (-5 * 6x + x * 6x)
5x + 5x2 = (-30x + 6x2)

Solving
5x + 5x2 = -30x + 6x2

Solving for variable 'x'.

Reorder the terms:
5x + 30x + 5x2 + -6x2 = -30x + 6x2 + 30x + -6x2

Combine like terms: 5x + 30x = 35x
35x + 5x2 + -6x2 = -30x + 6x2 + 30x + -6x2

Combine like terms: 5x2 + -6x2 = -1x2
35x + -1x2 = -30x + 6x2 + 30x + -6x2

Reorder the terms:
35x + -1x2 = -30x + 30x + 6x2 + -6x2

Combine like terms: -30x + 30x = 0
35x + -1x2 = 0 + 6x2 + -6x2
35x + -1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
35x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(35 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Solution
x = {0, 35}

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