-x^2-(x+1)(x+1)+85=0

Solution for -x^2-(x+1)(x+1)+85=0 equation:

Simplifying
-1x2 + -1(x + 1)(x + 1) + 85 = 0

Reorder the terms:
-1x2 + -1(1 + x)(x + 1) + 85 = 0

Reorder the terms:
-1x2 + -1(1 + x)(1 + x) + 85 = 0

Multiply (1 + x) * (1 + x)
-1x2 + -1(1(1 + x) + x(1 + x)) + 85 = 0
-1x2 + -1((1 * 1 + x * 1) + x(1 + x)) + 85 = 0
-1x2 + -1((1 + 1x) + x(1 + x)) + 85 = 0
-1x2 + -1(1 + 1x + (1 * x + x * x)) + 85 = 0
-1x2 + -1(1 + 1x + (1x + x2)) + 85 = 0

Combine like terms: 1x + 1x = 2x
-1x2 + -1(1 + 2x + x2) + 85 = 0
-1x2 + (1 * -1 + 2x * -1 + x2 * -1) + 85 = 0
-1x2 + (-1 + -2x + -1x2) + 85 = 0

Reorder the terms:
-1 + 85 + -2x + -1x2 + -1x2 = 0

Combine like terms: -1 + 85 = 84
84 + -2x + -1x2 + -1x2 = 0

Combine like terms: -1x2 + -1x2 = -2x2
84 + -2x + -2x2 = 0

Solving
84 + -2x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -1x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(7 + x)) = 0

Ignore the factor 2.
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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {6, -7}