(4r-5g)(4r+4g)=

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Solution for (4r-5g)(4r+4g)= equation: 


Simplifying
(4r + -5g)(4r + 4g) = 0

Reorder the terms:
(-5g + 4r)(4r + 4g) = 0

Reorder the terms:
(-5g + 4r)(4g + 4r) = 0

Multiply (-5g + 4r) * (4g + 4r)
(-5g * (4g + 4r) + 4r * (4g + 4r)) = 0
((4g * -5g + 4r * -5g) + 4r * (4g + 4r)) = 0

Reorder the terms:
((-20gr + -20g2) + 4r * (4g + 4r)) = 0
((-20gr + -20g2) + 4r * (4g + 4r)) = 0
(-20gr + -20g2 + (4g * 4r + 4r * 4r)) = 0
(-20gr + -20g2 + (16gr + 16r2)) = 0

Reorder the terms:
(-20gr + 16gr + -20g2 + 16r2) = 0

Combine like terms: -20gr + 16gr = -4gr
(-4gr + -20g2 + 16r2) = 0

Solving
-4gr + -20g2 + 16r2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1gr + -5g2 + 4r2) = 0

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

Ignore the factor 4.

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

Simplifying
-1g + -1r = 0

Solving
-1g + -1r = 0

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

Add 'r' to each side of the equation.
-1g + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-1g + 0 = 0 + r
-1g = 0 + r
Remove the zero:
-1g = r

Divide each side by '-1'.
g = -1r

Simplifying
g = -1r

Subproblem 2
Set the factor '(5g + -4r)' equal to zero and attempt to solve:

Simplifying
5g + -4r = 0

Solving
5g + -4r = 0

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

Add '4r' to each side of the equation.
5g + -4r + 4r = 0 + 4r

Combine like terms: -4r + 4r = 0
5g + 0 = 0 + 4r
5g = 0 + 4r
Remove the zero:
5g = 4r

Divide each side by '5'.
g = 0.8r

Simplifying
g = 0.8r
Solution
g = {-1r, 0.8r}

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