(x-7)(x+5)=-(x+23)

Solution for (x-7)(x+5)=-(x+23) equation:

Simplifying
(x + -7)(x + 5) = -1(x + 23)

Reorder the terms:
(-7 + x)(x + 5) = -1(x + 23)

Reorder the terms:
(-7 + x)(5 + x) = -1(x + 23)

Multiply (-7 + x) * (5 + x)
(-7(5 + x) + x(5 + x)) = -1(x + 23)
((5 * -7 + x * -7) + x(5 + x)) = -1(x + 23)
((-35 + -7x) + x(5 + x)) = -1(x + 23)
(-35 + -7x + (5 * x + x * x)) = -1(x + 23)
(-35 + -7x + (5x + x2)) = -1(x + 23)

Combine like terms: -7x + 5x = -2x
(-35 + -2x + x2) = -1(x + 23)

Reorder the terms:
-35 + -2x + x2 = -1(23 + x)
-35 + -2x + x2 = (23 * -1 + x * -1)
-35 + -2x + x2 = (-23 + -1x)

Solving
-35 + -2x + x2 = -23 + -1x

Solving for variable 'x'.

Reorder the terms:
-35 + 23 + -2x + x + x2 = -23 + -1x + 23 + x

Combine like terms: -35 + 23 = -12
-12 + -2x + x + x2 = -23 + -1x + 23 + x

Combine like terms: -2x + x = -1x
-12 + -1x + x2 = -23 + -1x + 23 + x

Reorder the terms:
-12 + -1x + x2 = -23 + 23 + -1x + x

Combine like terms: -23 + 23 = 0
-12 + -1x + x2 = 0 + -1x + x
-12 + -1x + x2 = -1x + x

Combine like terms: -1x + x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 4}