7v^2-14v=56

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Solution for 7v^2-14v=56 equation:


Simplifying
7v2 + -14v = 56

Reorder the terms:
-14v + 7v2 = 56

Solving
-14v + 7v2 = 56

Solving for variable 'v'.

Reorder the terms:
-56 + -14v + 7v2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -14v + 7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -2v + v2) = 0

Factor a trinomial.
7((-2 + -1v)(4 + -1v)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2

Subproblem 2

Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4

Solution

v = {-2, 4}

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