2c(c+4)=c^2+20

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Solution for 2c(c+4)=c^2+20 equation: 


Simplifying
2c(c + 4) = c2 + 20

Reorder the terms:
2c(4 + c) = c2 + 20
(4 * 2c + c * 2c) = c2 + 20
(8c + 2c2) = c2 + 20

Reorder the terms:
8c + 2c2 = 20 + c2

Solving
8c + 2c2 = 20 + c2

Solving for variable 'c'.

Reorder the terms:
-20 + 8c + 2c2 + -1c2 = 20 + c2 + -20 + -1c2

Combine like terms: 2c2 + -1c2 = 1c2
-20 + 8c + 1c2 = 20 + c2 + -20 + -1c2

Reorder the terms:
-20 + 8c + 1c2 = 20 + -20 + c2 + -1c2

Combine like terms: 20 + -20 = 0
-20 + 8c + 1c2 = 0 + c2 + -1c2
-20 + 8c + 1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
-20 + 8c + 1c2 = 0

Factor a trinomial.
(-10 + -1c)(2 + -1c) = 0


Subproblem 1
Set the factor '(-10 + -1c)' equal to zero and attempt to solve:

Simplifying
-10 + -1c = 0

Solving
-10 + -1c = 0

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

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

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

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

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

Simplifying
c = -10

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

Simplifying
2 + -1c = 0

Solving
2 + -1c = 0

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

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

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

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

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

Simplifying
c = 2
Solution
c = {-10, 2}

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