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Simplifying -5F(3F + 6)(9 + -2F) = 0 Reorder the terms: -5F(6 + 3F)(9 + -2F) = 0 Multiply (6 + 3F) * (9 + -2F) -5F(6(9 + -2F) + 3F * (9 + -2F)) = 0 -5F((9 * 6 + -2F * 6) + 3F * (9 + -2F)) = 0 -5F((54 + -12F) + 3F * (9 + -2F)) = 0 -5F(54 + -12F + (9 * 3F + -2F * 3F)) = 0 -5F(54 + -12F + (27F + -6F2)) = 0 Combine like terms: -12F + 27F = 15F -5F(54 + 15F + -6F2) = 0 (54 * -5F + 15F * -5F + -6F2 * -5F) = 0 (-270F + -75F2 + 30F3) = 0 Solving -270F + -75F2 + 30F3 = 0 Solving for variable 'F'. Factor out the Greatest Common Factor (GCF), '15F'. 15F(-18 + -5F + 2F2) = 0 Factor a trinomial. 15F((-2 + -1F)(9 + -2F)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'F' equal to zero and attempt to solve: Simplifying F = 0 Solving F = 0 Move all terms containing F to the left, all other terms to the right. Simplifying F = 0Subproblem 2
Set the factor '(-2 + -1F)' equal to zero and attempt to solve: Simplifying -2 + -1F = 0 Solving -2 + -1F = 0 Move all terms containing F to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1F = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1F = 0 + 2 -1F = 0 + 2 Combine like terms: 0 + 2 = 2 -1F = 2 Divide each side by '-1'. F = -2 Simplifying F = -2Subproblem 3
Set the factor '(9 + -2F)' equal to zero and attempt to solve: Simplifying 9 + -2F = 0 Solving 9 + -2F = 0 Move all terms containing F to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2F = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2F = 0 + -9 -2F = 0 + -9 Combine like terms: 0 + -9 = -9 -2F = -9 Divide each side by '-2'. F = 4.5 Simplifying F = 4.5Solution
F = {0, -2, 4.5}
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