5(x-11)=2x(11-x)1

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Solution for 5(x-11)=2x(11-x)1 equation: 


Simplifying
5(x + -11) = 2x(11 + -1x) * 1

Reorder the terms:
5(-11 + x) = 2x(11 + -1x) * 1
(-11 * 5 + x * 5) = 2x(11 + -1x) * 1
(-55 + 5x) = 2x(11 + -1x) * 1

Reorder the terms for easier multiplication:
-55 + 5x = 2 * 1x(11 + -1x)

Multiply 2 * 1
-55 + 5x = 2x(11 + -1x)
-55 + 5x = (11 * 2x + -1x * 2x)
-55 + 5x = (22x + -2x2)

Solving
-55 + 5x = 22x + -2x2

Solving for variable 'x'.

Combine like terms: 5x + -22x = -17x
-55 + -17x + 2x2 = 22x + -2x2 + -22x + 2x2

Reorder the terms:
-55 + -17x + 2x2 = 22x + -22x + -2x2 + 2x2

Combine like terms: 22x + -22x = 0
-55 + -17x + 2x2 = 0 + -2x2 + 2x2
-55 + -17x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-55 + -17x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-2.5, 11}

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