(x+7)(x-5)=-11

Solution for (x+7)(x-5)=-11 equation:

Simplifying
(x + 7)(x + -5) = -11

Reorder the terms:
(7 + x)(x + -5) = -11

Reorder the terms:
(7 + x)(-5 + x) = -11

Multiply (7 + x) * (-5 + x)
(7(-5 + x) + x(-5 + x)) = -11
((-5 * 7 + x * 7) + x(-5 + x)) = -11
((-35 + 7x) + x(-5 + x)) = -11
(-35 + 7x + (-5 * x + x * x)) = -11
(-35 + 7x + (-5x + x2)) = -11

Combine like terms: 7x + -5x = 2x
(-35 + 2x + x2) = -11

Solving
-35 + 2x + x2 = -11

Solving for variable 'x'.

Reorder the terms:
-35 + 11 + 2x + x2 = -11 + 11

Combine like terms: -35 + 11 = -24
-24 + 2x + x2 = -11 + 11

Combine like terms: -11 + 11 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -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 '(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
Solution
x = {-6, 4}