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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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