(x)(x+1)=14(2x+1)+44

Solution for (x)(x+1)=14(2x+1)+44 equation:

Simplifying
(x)(x + 1) = 14(2x + 1) + 44

Reorder the terms:
x(1 + x) = 14(2x + 1) + 44
(1 * x + x * x) = 14(2x + 1) + 44
(1x + x2) = 14(2x + 1) + 44

Reorder the terms:
1x + x2 = 14(1 + 2x) + 44
1x + x2 = (1 * 14 + 2x * 14) + 44
1x + x2 = (14 + 28x) + 44

Reorder the terms:
1x + x2 = 14 + 44 + 28x

Combine like terms: 14 + 44 = 58
1x + x2 = 58 + 28x

Solving
1x + x2 = 58 + 28x

Solving for variable 'x'.

Reorder the terms:
-58 + 1x + -28x + x2 = 58 + 28x + -58 + -28x

Combine like terms: 1x + -28x = -27x
-58 + -27x + x2 = 58 + 28x + -58 + -28x

Reorder the terms:
-58 + -27x + x2 = 58 + -58 + 28x + -28x

Combine like terms: 58 + -58 = 0
-58 + -27x + x2 = 0 + 28x + -28x
-58 + -27x + x2 = 28x + -28x

Combine like terms: 28x + -28x = 0
-58 + -27x + x2 = 0

Factor a trinomial.
(-2 + -1x)(29 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(29 + -1x)' equal to zero and attempt to solve:

Simplifying
29 + -1x = 0

Solving
29 + -1x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -1x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -1x = 0 + -29
-1x = 0 + -29

Combine like terms: 0 + -29 = -29
-1x = -29

Divide each side by '-1'.
x = 29

Simplifying
x = 29
Solution
x = {-2, 29}