2(x+17)=11x+2(x^2-17)

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Solution for 2(x+17)=11x+2(x^2-17) equation: 


Simplifying
2(x + 17) = 11x + 2(x2 + -17)

Reorder the terms:
2(17 + x) = 11x + 2(x2 + -17)
(17 * 2 + x * 2) = 11x + 2(x2 + -17)
(34 + 2x) = 11x + 2(x2 + -17)

Reorder the terms:
34 + 2x = 11x + 2(-17 + x2)
34 + 2x = 11x + (-17 * 2 + x2 * 2)
34 + 2x = 11x + (-34 + 2x2)

Reorder the terms:
34 + 2x = -34 + 11x + 2x2

Solving
34 + 2x = -34 + 11x + 2x2

Solving for variable 'x'.

Reorder the terms:
34 + 34 + 2x + -11x + -2x2 = -34 + 11x + 2x2 + 34 + -11x + -2x2

Combine like terms: 34 + 34 = 68
68 + 2x + -11x + -2x2 = -34 + 11x + 2x2 + 34 + -11x + -2x2

Combine like terms: 2x + -11x = -9x
68 + -9x + -2x2 = -34 + 11x + 2x2 + 34 + -11x + -2x2

Reorder the terms:
68 + -9x + -2x2 = -34 + 34 + 11x + -11x + 2x2 + -2x2

Combine like terms: -34 + 34 = 0
68 + -9x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2
68 + -9x + -2x2 = 11x + -11x + 2x2 + -2x2

Combine like terms: 11x + -11x = 0
68 + -9x + -2x2 = 0 + 2x2 + -2x2
68 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
68 + -9x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(17 + 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 '(17 + 2x)' equal to zero and attempt to solve:

Simplifying
17 + 2x = 0

Solving
17 + 2x = 0

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

Add '-17' to each side of the equation.
17 + -17 + 2x = 0 + -17

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

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

Divide each side by '2'.
x = -8.5

Simplifying
x = -8.5
Solution
x = {4, -8.5}

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