-11x(x-5)=55-11x

Solution for -11x(x-5)=55-11x equation:

Simplifying
-11x(x + -5) = 55 + -11x

Reorder the terms:
-11x(-5 + x) = 55 + -11x
(-5 * -11x + x * -11x) = 55 + -11x
(55x + -11x2) = 55 + -11x

Solving
55x + -11x2 = 55 + -11x

Solving for variable 'x'.

Reorder the terms:
-55 + 55x + 11x + -11x2 = 55 + -11x + -55 + 11x

Combine like terms: 55x + 11x = 66x
-55 + 66x + -11x2 = 55 + -11x + -55 + 11x

Reorder the terms:
-55 + 66x + -11x2 = 55 + -55 + -11x + 11x

Combine like terms: 55 + -55 = 0
-55 + 66x + -11x2 = 0 + -11x + 11x
-55 + 66x + -11x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
-55 + 66x + -11x2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(-5 + 6x + -1x2) = 0

Factor a trinomial.
11((-5 + x)(1 + -1x)) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5
Subproblem 2
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
Solution
x = {5, 1}