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

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


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

Reorder the terms:
5x + 6x(-6 + x) = 5(x + -6)
5x + (-6 * 6x + x * 6x) = 5(x + -6)
5x + (-36x + 6x2) = 5(x + -6)

Combine like terms: 5x + -36x = -31x
-31x + 6x2 = 5(x + -6)

Reorder the terms:
-31x + 6x2 = 5(-6 + x)
-31x + 6x2 = (-6 * 5 + x * 5)
-31x + 6x2 = (-30 + 5x)

Solving
-31x + 6x2 = -30 + 5x

Solving for variable 'x'.

Reorder the terms:
30 + -31x + -5x + 6x2 = -30 + 5x + 30 + -5x

Combine like terms: -31x + -5x = -36x
30 + -36x + 6x2 = -30 + 5x + 30 + -5x

Reorder the terms:
30 + -36x + 6x2 = -30 + 30 + 5x + -5x

Combine like terms: -30 + 30 = 0
30 + -36x + 6x2 = 0 + 5x + -5x
30 + -36x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
30 + -36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -6x + x2) = 0

Factor a trinomial.
6((1 + -1x)(5 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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, 5}

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