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Simplifying 4v2 + 25vz + 6z2 = 0 Reorder the terms: 25vz + 4v2 + 6z2 = 0 Solving 25vz + 4v2 + 6z2 = 0 Solving for variable 'v'. Factor a trinomial. (4v + z)(v + 6z) = 0Subproblem 1
Set the factor '(4v + z)' equal to zero and attempt to solve: Simplifying 4v + z = 0 Solving 4v + z = 0 Move all terms containing v to the left, all other terms to the right. Add '-1z' to each side of the equation. 4v + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 4v + 0 = 0 + -1z 4v = 0 + -1z Remove the zero: 4v = -1z Divide each side by '4'. v = -0.25z Simplifying v = -0.25zSubproblem 2
Set the factor '(v + 6z)' equal to zero and attempt to solve: Simplifying v + 6z = 0 Solving v + 6z = 0 Move all terms containing v to the left, all other terms to the right. Add '-6z' to each side of the equation. v + 6z + -6z = 0 + -6z Combine like terms: 6z + -6z = 0 v + 0 = 0 + -6z v = 0 + -6z Remove the zero: v = -6z Simplifying v = -6zSolution
v = {-0.25z, -6z}
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