X(X+2)=35+8(X+X+2)

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Solution for X(X+2)=35+8(X+X+2) equation: 


Simplifying
X(X + 2) = 35 + 8(X + X + 2)

Reorder the terms:
X(2 + X) = 35 + 8(X + X + 2)
(2 * X + X * X) = 35 + 8(X + X + 2)
(2X + X2) = 35 + 8(X + X + 2)

Reorder the terms:
2X + X2 = 35 + 8(2 + X + X)

Combine like terms: X + X = 2X
2X + X2 = 35 + 8(2 + 2X)
2X + X2 = 35 + (2 * 8 + 2X * 8)
2X + X2 = 35 + (16 + 16X)

Combine like terms: 35 + 16 = 51
2X + X2 = 51 + 16X

Solving
2X + X2 = 51 + 16X

Solving for variable 'X'.

Reorder the terms:
-51 + 2X + -16X + X2 = 51 + 16X + -51 + -16X

Combine like terms: 2X + -16X = -14X
-51 + -14X + X2 = 51 + 16X + -51 + -16X

Reorder the terms:
-51 + -14X + X2 = 51 + -51 + 16X + -16X

Combine like terms: 51 + -51 = 0
-51 + -14X + X2 = 0 + 16X + -16X
-51 + -14X + X2 = 16X + -16X

Combine like terms: 16X + -16X = 0
-51 + -14X + X2 = 0

Factor a trinomial.
(-3 + -1X)(17 + -1X) = 0


Subproblem 1
Set the factor '(-3 + -1X)' equal to zero and attempt to solve:

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X = 0 + 3
-1X = 0 + 3

Combine like terms: 0 + 3 = 3
-1X = 3

Divide each side by '-1'.
X = -3

Simplifying
X = -3

Subproblem 2
Set the factor '(17 + -1X)' equal to zero and attempt to solve:

Simplifying
17 + -1X = 0

Solving
17 + -1X = 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 + -1X = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1X = 0 + -17
-1X = 0 + -17

Combine like terms: 0 + -17 = -17
-1X = -17

Divide each side by '-1'.
X = 17

Simplifying
X = 17
Solution
X = {-3, 17}

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