x^2-21x+78=-3x-2

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Solution for x^2-21x+78=-3x-2 equation: 


Simplifying
x2 + -21x + 78 = -3x + -2

Reorder the terms:
78 + -21x + x2 = -3x + -2

Reorder the terms:
78 + -21x + x2 = -2 + -3x

Solving
78 + -21x + x2 = -2 + -3x

Solving for variable 'x'.

Reorder the terms:
78 + 2 + -21x + 3x + x2 = -2 + -3x + 2 + 3x

Combine like terms: 78 + 2 = 80
80 + -21x + 3x + x2 = -2 + -3x + 2 + 3x

Combine like terms: -21x + 3x = -18x
80 + -18x + x2 = -2 + -3x + 2 + 3x

Reorder the terms:
80 + -18x + x2 = -2 + 2 + -3x + 3x

Combine like terms: -2 + 2 = 0
80 + -18x + x2 = 0 + -3x + 3x
80 + -18x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
80 + -18x + 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}

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