v^2-2v=24+3v

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Solution for v^2-2v=24+3v equation:


Simplifying
v2 + -2v = 24 + 3v

Reorder the terms:
-2v + v2 = 24 + 3v

Solving
-2v + v2 = 24 + 3v

Solving for variable 'v'.

Reorder the terms:
-24 + -2v + -3v + v2 = 24 + 3v + -24 + -3v

Combine like terms: -2v + -3v = -5v
-24 + -5v + v2 = 24 + 3v + -24 + -3v

Reorder the terms:
-24 + -5v + v2 = 24 + -24 + 3v + -3v

Combine like terms: 24 + -24 = 0
-24 + -5v + v2 = 0 + 3v + -3v
-24 + -5v + v2 = 3v + -3v

Combine like terms: 3v + -3v = 0
-24 + -5v + v2 = 0

Factor a trinomial.
(-3 + -1v)(8 + -1v) = 0

Subproblem 1

Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3

Subproblem 2

Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8

Solution

v = {-3, 8}

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