(7g-d)(2g-4d)=

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Solution for (7g-d)(2g-4d)= equation: 


Simplifying
(7g + -1d)(2g + -4d) = 0

Reorder the terms:
(-1d + 7g)(2g + -4d) = 0

Reorder the terms:
(-1d + 7g)(-4d + 2g) = 0

Multiply (-1d + 7g) * (-4d + 2g)
(-1d * (-4d + 2g) + 7g * (-4d + 2g)) = 0
((-4d * -1d + 2g * -1d) + 7g * (-4d + 2g)) = 0

Reorder the terms:
((-2dg + 4d2) + 7g * (-4d + 2g)) = 0
((-2dg + 4d2) + 7g * (-4d + 2g)) = 0
(-2dg + 4d2 + (-4d * 7g + 2g * 7g)) = 0
(-2dg + 4d2 + (-28dg + 14g2)) = 0

Reorder the terms:
(-2dg + -28dg + 4d2 + 14g2) = 0

Combine like terms: -2dg + -28dg = -30dg
(-30dg + 4d2 + 14g2) = 0

Solving
-30dg + 4d2 + 14g2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15dg + 2d2 + 7g2) = 0

Factor a trinomial.
2((d + -7g)(2d + -1g)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(d + -7g)' equal to zero and attempt to solve:

Simplifying
d + -7g = 0

Solving
d + -7g = 0

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

Add '7g' to each side of the equation.
d + -7g + 7g = 0 + 7g

Combine like terms: -7g + 7g = 0
d + 0 = 0 + 7g
d = 0 + 7g
Remove the zero:
d = 7g

Simplifying
d = 7g

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

Simplifying
2d + -1g = 0

Solving
2d + -1g = 0

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

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

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

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

Simplifying
d = 0.5g
Solution
d = {7g, 0.5g}

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