(4f*5f-3g)*4f*(5f+4f*6g)=

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Solution for (4f*5f-3g)*4f*(5f+4f*6g)= equation: 


Simplifying
(4f * 5f + -3g) * 4f(5f + 4f * 6g) = 0

Reorder the terms for easier multiplication:
(4 * 5f * f + -3g) * 4f(5f + 4f * 6g) = 0

Multiply 4 * 5
(20f * f + -3g) * 4f(5f + 4f * 6g) = 0

Multiply f * f
(20f2 + -3g) * 4f(5f + 4f * 6g) = 0

Reorder the terms for easier multiplication:
(20f2 + -3g) * 4f(5f + 4 * 6f * g) = 0

Multiply 4 * 6
(20f2 + -3g) * 4f(5f + 24f * g) = 0

Multiply f * g
(20f2 + -3g) * 4f(5f + 24fg) = 0

Reorder the terms for easier multiplication:
4f(20f2 + -3g)(5f + 24fg) = 0

Multiply (20f2 + -3g) * (5f + 24fg)
4f(20f2 * (5f + 24fg) + -3g * (5f + 24fg)) = 0
4f((5f * 20f2 + 24fg * 20f2) + -3g * (5f + 24fg)) = 0
4f((100f3 + 480f3g) + -3g * (5f + 24fg)) = 0
4f(100f3 + 480f3g + (5f * -3g + 24fg * -3g)) = 0
4f(100f3 + 480f3g + (-15fg + -72fg2)) = 0

Reorder the terms:
4f(-15fg + -72fg2 + 100f3 + 480f3g) = 0
4f(-15fg + -72fg2 + 100f3 + 480f3g) = 0
(-15fg * 4f + -72fg2 * 4f + 100f3 * 4f + 480f3g * 4f) = 0
(-60f2g + -288f2g2 + 400f4 + 1920f4g) = 0

Solving
-60f2g + -288f2g2 + 400f4 + 1920f4g = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4f2'.
4f2(-15g + -72g2 + 100f2 + 480f2g) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'f2' equal to zero and attempt to solve:

Simplifying
f2 = 0

Solving
f2 = 0

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

Simplifying
f2 = 0

Take the square root of each side:
f = {0}

Subproblem 2
Set the factor '(-15g + -72g2 + 100f2 + 480f2g)' equal to zero and attempt to solve:

Simplifying
-15g + -72g2 + 100f2 + 480f2g = 0

Reorder the terms:
100f2 + 480f2g + -15g + -72g2 = 0

Solving
100f2 + 480f2g + -15g + -72g2 = 0

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

Add '15g' to each side of the equation.
100f2 + 480f2g + -15g + 15g + -72g2 = 0 + 15g

Combine like terms: -15g + 15g = 0
100f2 + 480f2g + 0 + -72g2 = 0 + 15g
100f2 + 480f2g + -72g2 = 0 + 15g
Remove the zero:
100f2 + 480f2g + -72g2 = 15g

Add '72g2' to each side of the equation.
100f2 + 480f2g + -72g2 + 72g2 = 15g + 72g2

Combine like terms: -72g2 + 72g2 = 0
100f2 + 480f2g + 0 = 15g + 72g2
100f2 + 480f2g = 15g + 72g2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
f = {0}

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