2(x+11)=5x+2(x^2-11)

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


Simplifying
2(x + 11) = 5x + 2(x2 + -11)

Reorder the terms:
2(11 + x) = 5x + 2(x2 + -11)
(11 * 2 + x * 2) = 5x + 2(x2 + -11)
(22 + 2x) = 5x + 2(x2 + -11)

Reorder the terms:
22 + 2x = 5x + 2(-11 + x2)
22 + 2x = 5x + (-11 * 2 + x2 * 2)
22 + 2x = 5x + (-22 + 2x2)

Reorder the terms:
22 + 2x = -22 + 5x + 2x2

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

Solving for variable 'x'.

Reorder the terms:
22 + 22 + 2x + -5x + -2x2 = -22 + 5x + 2x2 + 22 + -5x + -2x2

Combine like terms: 22 + 22 = 44
44 + 2x + -5x + -2x2 = -22 + 5x + 2x2 + 22 + -5x + -2x2

Combine like terms: 2x + -5x = -3x
44 + -3x + -2x2 = -22 + 5x + 2x2 + 22 + -5x + -2x2

Reorder the terms:
44 + -3x + -2x2 = -22 + 22 + 5x + -5x + 2x2 + -2x2

Combine like terms: -22 + 22 = 0
44 + -3x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
44 + -3x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
44 + -3x + -2x2 = 0 + 2x2 + -2x2
44 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
44 + -3x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(11 + 2x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
11 + 2x = 0

Solving
11 + 2x = 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 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Solution
x = {4, -5.5}

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