(x-9)(x+7)=-(x+43)

Solution for (x-9)(x+7)=-(x+43) equation:

Simplifying
(x + -9)(x + 7) = -1(x + 43)

Reorder the terms:
(-9 + x)(x + 7) = -1(x + 43)

Reorder the terms:
(-9 + x)(7 + x) = -1(x + 43)

Multiply (-9 + x) * (7 + x)
(-9(7 + x) + x(7 + x)) = -1(x + 43)
((7 * -9 + x * -9) + x(7 + x)) = -1(x + 43)
((-63 + -9x) + x(7 + x)) = -1(x + 43)
(-63 + -9x + (7 * x + x * x)) = -1(x + 43)
(-63 + -9x + (7x + x2)) = -1(x + 43)

Combine like terms: -9x + 7x = -2x
(-63 + -2x + x2) = -1(x + 43)

Reorder the terms:
-63 + -2x + x2 = -1(43 + x)
-63 + -2x + x2 = (43 * -1 + x * -1)
-63 + -2x + x2 = (-43 + -1x)

Solving
-63 + -2x + x2 = -43 + -1x

Solving for variable 'x'.

Reorder the terms:
-63 + 43 + -2x + x + x2 = -43 + -1x + 43 + x

Combine like terms: -63 + 43 = -20
-20 + -2x + x + x2 = -43 + -1x + 43 + x

Combine like terms: -2x + x = -1x
-20 + -1x + x2 = -43 + -1x + 43 + x

Reorder the terms:
-20 + -1x + x2 = -43 + 43 + -1x + x

Combine like terms: -43 + 43 = 0
-20 + -1x + x2 = 0 + -1x + x
-20 + -1x + x2 = -1x + x

Combine like terms: -1x + x = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4, 5}