x^2-4x-77=(x+7)

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Solution for x^2-4x-77=(x+7) equation: 


Simplifying
x2 + -4x + -77 = (x + 7)

Reorder the terms:
-77 + -4x + x2 = (x + 7)

Reorder the terms:
-77 + -4x + x2 = (7 + x)

Remove parenthesis around (7 + x)
-77 + -4x + x2 = 7 + x

Solving
-77 + -4x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-77 + -7 + -4x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -77 + -7 = -84
-84 + -4x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -4x + -1x = -5x
-84 + -5x + x2 = 7 + x + -7 + -1x

Reorder the terms:
-84 + -5x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-84 + -5x + x2 = 0 + x + -1x
-84 + -5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-84 + -5x + x2 = 0

Factor a trinomial.
(-7 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-7, 12}

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