(x+6)(x-9)=34

Solution for (x+6)(x-9)=34 equation:

Simplifying
(x + 6)(x + -9) = 34

Reorder the terms:
(6 + x)(x + -9) = 34

Reorder the terms:
(6 + x)(-9 + x) = 34

Multiply (6 + x) * (-9 + x)
(6(-9 + x) + x(-9 + x)) = 34
((-9 * 6 + x * 6) + x(-9 + x)) = 34
((-54 + 6x) + x(-9 + x)) = 34
(-54 + 6x + (-9 * x + x * x)) = 34
(-54 + 6x + (-9x + x2)) = 34

Combine like terms: 6x + -9x = -3x
(-54 + -3x + x2) = 34

Solving
-54 + -3x + x2 = 34

Solving for variable 'x'.

Reorder the terms:
-54 + -34 + -3x + x2 = 34 + -34

Combine like terms: -54 + -34 = -88
-88 + -3x + x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-88 + -3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-8, 11}