x(x+1)=68+2(x+2)

Solution for x(x+1)=68+2(x+2) equation:

Simplifying
x(x + 1) = 68 + 2(x + 2)

Reorder the terms:
x(1 + x) = 68 + 2(x + 2)
(1 * x + x * x) = 68 + 2(x + 2)
(1x + x2) = 68 + 2(x + 2)

Reorder the terms:
1x + x2 = 68 + 2(2 + x)
1x + x2 = 68 + (2 * 2 + x * 2)
1x + x2 = 68 + (4 + 2x)

Combine like terms: 68 + 4 = 72
1x + x2 = 72 + 2x

Solving
1x + x2 = 72 + 2x

Solving for variable 'x'.

Reorder the terms:
-72 + 1x + -2x + x2 = 72 + 2x + -72 + -2x

Combine like terms: 1x + -2x = -1x
-72 + -1x + x2 = 72 + 2x + -72 + -2x

Reorder the terms:
-72 + -1x + x2 = 72 + -72 + 2x + -2x

Combine like terms: 72 + -72 = 0
-72 + -1x + x2 = 0 + 2x + -2x
-72 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-72 + -1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-8, 9}