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Simplifying 105v4 + 162v3 + 21v2 = 0 Reorder the terms: 21v2 + 162v3 + 105v4 = 0 Solving 21v2 + 162v3 + 105v4 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3v2'. 3v2(7 + 54v + 35v2) = 0 Factor a trinomial. 3v2((7 + 5v)(1 + 7v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve: Simplifying v2 = 0 Solving v2 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v2 = 0 Take the square root of each side: v = {0}Subproblem 2
Set the factor '(7 + 5v)' equal to zero and attempt to solve: Simplifying 7 + 5v = 0 Solving 7 + 5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5v = 0 + -7 5v = 0 + -7 Combine like terms: 0 + -7 = -7 5v = -7 Divide each side by '5'. v = -1.4 Simplifying v = -1.4Subproblem 3
Set the factor '(1 + 7v)' equal to zero and attempt to solve: Simplifying 1 + 7v = 0 Solving 1 + 7v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7v = 0 + -1 7v = 0 + -1 Combine like terms: 0 + -1 = -1 7v = -1 Divide each side by '7'. v = -0.1428571429 Simplifying v = -0.1428571429Solution
v = {0, -1.4, -0.1428571429}
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