(c-2)(4c+5)=0

Solution for (c-2)(4c+5)=0 equation:

Simplifying
(c + -2)(4c + 5) = 0

Reorder the terms:
(-2 + c)(4c + 5) = 0

Reorder the terms:
(-2 + c)(5 + 4c) = 0

Multiply (-2 + c) * (5 + 4c)
(-2(5 + 4c) + c(5 + 4c)) = 0
((5 * -2 + 4c * -2) + c(5 + 4c)) = 0
((-10 + -8c) + c(5 + 4c)) = 0
(-10 + -8c + (5 * c + 4c * c)) = 0
(-10 + -8c + (5c + 4c2)) = 0

Combine like terms: -8c + 5c = -3c
(-10 + -3c + 4c2) = 0

Solving
-10 + -3c + 4c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-5 + -4c)(2 + -1c) = 0

Subproblem 1
Set the factor '(-5 + -4c)' equal to zero and attempt to solve:

Simplifying
-5 + -4c = 0

Solving
-5 + -4c = 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 + -4c = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4c = 0 + 5
-4c = 0 + 5

Combine like terms: 0 + 5 = 5
-4c = 5

Divide each side by '-4'.
c = -1.25

Simplifying
c = -1.25
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 = {-1.25, 2}