-(x+9)(x-7)=55

Solution for -(x+9)(x-7)=55 equation:

Simplifying
-1(x + 9)(x + -7) = 55

Reorder the terms:
-1(9 + x)(x + -7) = 55

Reorder the terms:
-1(9 + x)(-7 + x) = 55

Multiply (9 + x) * (-7 + x)
-1(9(-7 + x) + x(-7 + x)) = 55
-1((-7 * 9 + x * 9) + x(-7 + x)) = 55
-1((-63 + 9x) + x(-7 + x)) = 55
-1(-63 + 9x + (-7 * x + x * x)) = 55
-1(-63 + 9x + (-7x + x2)) = 55

Combine like terms: 9x + -7x = 2x
-1(-63 + 2x + x2) = 55
(-63 * -1 + 2x * -1 + x2 * -1) = 55
(63 + -2x + -1x2) = 55

Solving
63 + -2x + -1x2 = 55

Solving for variable 'x'.

Reorder the terms:
63 + -55 + -2x + -1x2 = 55 + -55

Combine like terms: 63 + -55 = 8
8 + -2x + -1x2 = 55 + -55

Combine like terms: 55 + -55 = 0
8 + -2x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(4 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {2, -4}