(-2c+d)(c+2d)=

Solution for (-2c+d)(c+2d)= equation:

Simplifying
(-2c + d)(c + 2d) = 0

Multiply (-2c + d) * (c + 2d)
(-2c * (c + 2d) + d(c + 2d)) = 0
((c * -2c + 2d * -2c) + d(c + 2d)) = 0

Reorder the terms:
((-4cd + -2c2) + d(c + 2d)) = 0
((-4cd + -2c2) + d(c + 2d)) = 0
(-4cd + -2c2 + (c * d + 2d * d)) = 0
(-4cd + -2c2 + (cd + 2d2)) = 0

Reorder the terms:
(-4cd + cd + -2c2 + 2d2) = 0

Combine like terms: -4cd + cd = -3cd
(-3cd + -2c2 + 2d2) = 0

Solving
-3cd + -2c2 + 2d2 = 0

Solving for variable 'c'.

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

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

Simplifying
-1c + -2d = 0

Solving
-1c + -2d = 0

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

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

Combine like terms: -2d + 2d = 0
-1c + 0 = 0 + 2d
-1c = 0 + 2d
Remove the zero:
-1c = 2d

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

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

Simplifying
2c + -1d = 0

Solving
2c + -1d = 0

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

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

Combine like terms: -1d + d = 0
2c + 0 = 0 + d
2c = 0 + d
Remove the zero:
2c = d

Divide each side by '2'.
c = 0.5d

Simplifying
c = 0.5d
Solution
c = {-2d, 0.5d}