2(x+19)=13x+2(x^2-19)

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Solution for 2(x+19)=13x+2(x^2-19) equation: 


Simplifying
2(x + 19) = 13x + 2(x2 + -19)

Reorder the terms:
2(19 + x) = 13x + 2(x2 + -19)
(19 * 2 + x * 2) = 13x + 2(x2 + -19)
(38 + 2x) = 13x + 2(x2 + -19)

Reorder the terms:
38 + 2x = 13x + 2(-19 + x2)
38 + 2x = 13x + (-19 * 2 + x2 * 2)
38 + 2x = 13x + (-38 + 2x2)

Reorder the terms:
38 + 2x = -38 + 13x + 2x2

Solving
38 + 2x = -38 + 13x + 2x2

Solving for variable 'x'.

Reorder the terms:
38 + 38 + 2x + -13x + -2x2 = -38 + 13x + 2x2 + 38 + -13x + -2x2

Combine like terms: 38 + 38 = 76
76 + 2x + -13x + -2x2 = -38 + 13x + 2x2 + 38 + -13x + -2x2

Combine like terms: 2x + -13x = -11x
76 + -11x + -2x2 = -38 + 13x + 2x2 + 38 + -13x + -2x2

Reorder the terms:
76 + -11x + -2x2 = -38 + 38 + 13x + -13x + 2x2 + -2x2

Combine like terms: -38 + 38 = 0
76 + -11x + -2x2 = 0 + 13x + -13x + 2x2 + -2x2
76 + -11x + -2x2 = 13x + -13x + 2x2 + -2x2

Combine like terms: 13x + -13x = 0
76 + -11x + -2x2 = 0 + 2x2 + -2x2
76 + -11x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
76 + -11x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(19 + 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 '(19 + 2x)' equal to zero and attempt to solve:

Simplifying
19 + 2x = 0

Solving
19 + 2x = 0

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

Add '-19' to each side of the equation.
19 + -19 + 2x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 2x = 0 + -19
2x = 0 + -19

Combine like terms: 0 + -19 = -19
2x = -19

Divide each side by '2'.
x = -9.5

Simplifying
x = -9.5
Solution
x = {4, -9.5}

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