(x-11)(x+4)=34

Solution for (x-11)(x+4)=34 equation:

Simplifying
(x + -11)(x + 4) = 34

Reorder the terms:
(-11 + x)(x + 4) = 34

Reorder the terms:
(-11 + x)(4 + x) = 34

Multiply (-11 + x) * (4 + x)
(-11(4 + x) + x(4 + x)) = 34
((4 * -11 + x * -11) + x(4 + x)) = 34
((-44 + -11x) + x(4 + x)) = 34
(-44 + -11x + (4 * x + x * x)) = 34
(-44 + -11x + (4x + x2)) = 34

Combine like terms: -11x + 4x = -7x
(-44 + -7x + x2) = 34

Solving
-44 + -7x + x2 = 34

Solving for variable 'x'.

Reorder the terms:
-44 + -34 + -7x + x2 = 34 + -34

Combine like terms: -44 + -34 = -78
-78 + -7x + x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-78 + -7x + x2 = 0

Factor a trinomial.
(-6 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-6, 13}