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

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

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

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

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

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

Combine like terms: 9x + -6x = 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.
(-11 + -1x)(8 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-11, 8}