c^2+c=2c+20

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Solution for c^2+c=2c+20 equation:


Simplifying
c2 + c = 2c + 20

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

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

Solving
c + c2 = 20 + 2c

Solving for variable 'c'.

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

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

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

Combine like terms: 20 + -20 = 0
-20 + -1c + c2 = 0 + 2c + -2c
-20 + -1c + c2 = 2c + -2c

Combine like terms: 2c + -2c = 0
-20 + -1c + c2 = 0

Factor a trinomial.
(-4 + -1c)(5 + -1c) = 0

Subproblem 1

Set the factor '(-4 + -1c)' equal to zero and attempt to solve: Simplifying -4 + -1c = 0 Solving -4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1c = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1c = 0 + 4 -1c = 0 + 4 Combine like terms: 0 + 4 = 4 -1c = 4 Divide each side by '-1'. c = -4 Simplifying c = -4

Subproblem 2

Set the factor '(5 + -1c)' equal to zero and attempt to solve: Simplifying 5 + -1c = 0 Solving 5 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1c = 0 + -5 -1c = 0 + -5 Combine like terms: 0 + -5 = -5 -1c = -5 Divide each side by '-1'. c = 5 Simplifying c = 5

Solution

c = {-4, 5}

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