x(x+1)-3(x+1)=77

Solution for x(x+1)-3(x+1)=77 equation:

Simplifying
x(x + 1) + -3(x + 1) = 77

Reorder the terms:
x(1 + x) + -3(x + 1) = 77
(1 * x + x * x) + -3(x + 1) = 77
(1x + x2) + -3(x + 1) = 77

Reorder the terms:
1x + x2 + -3(1 + x) = 77
1x + x2 + (1 * -3 + x * -3) = 77
1x + x2 + (-3 + -3x) = 77

Reorder the terms:
-3 + 1x + -3x + x2 = 77

Combine like terms: 1x + -3x = -2x
-3 + -2x + x2 = 77

Solving
-3 + -2x + x2 = 77

Solving for variable 'x'.

Reorder the terms:
-3 + -77 + -2x + x2 = 77 + -77

Combine like terms: -3 + -77 = -80
-80 + -2x + x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-80 + -2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-8, 10}