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

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

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

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

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

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

Combine like terms: -4x + 11x = 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.
(-13 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-13, 6}