5v^2-10v=315

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Solution for 5v^2-10v=315 equation:


Simplifying
5v2 + -10v = 315

Reorder the terms:
-10v + 5v2 = 315

Solving
-10v + 5v2 = 315

Solving for variable 'v'.

Reorder the terms:
-315 + -10v + 5v2 = 315 + -315

Combine like terms: 315 + -315 = 0
-315 + -10v + 5v2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-63 + -2v + v2) = 0

Factor a trinomial.
5((-7 + -1v)(9 + -1v)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 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 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7

Subproblem 2

Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9

Solution

v = {-7, 9}

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