(x+2)(x+3)=8x+34

Solution for (x+2)(x+3)=8x+34 equation:

Simplifying
(x + 2)(x + 3) = 8x + 34

Reorder the terms:
(2 + x)(x + 3) = 8x + 34

Reorder the terms:
(2 + x)(3 + x) = 8x + 34

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 8x + 34
((3 * 2 + x * 2) + x(3 + x)) = 8x + 34
((6 + 2x) + x(3 + x)) = 8x + 34
(6 + 2x + (3 * x + x * x)) = 8x + 34
(6 + 2x + (3x + x2)) = 8x + 34

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 8x + 34

Reorder the terms:
6 + 5x + x2 = 34 + 8x

Solving
6 + 5x + x2 = 34 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + -34 + 5x + -8x + x2 = 34 + 8x + -34 + -8x

Combine like terms: 6 + -34 = -28
-28 + 5x + -8x + x2 = 34 + 8x + -34 + -8x

Combine like terms: 5x + -8x = -3x
-28 + -3x + x2 = 34 + 8x + -34 + -8x

Reorder the terms:
-28 + -3x + x2 = 34 + -34 + 8x + -8x

Combine like terms: 34 + -34 = 0
-28 + -3x + x2 = 0 + 8x + -8x
-28 + -3x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-28 + -3x + x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-4, 7}