3v^2+10v-45=12

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Solution for 3v^2+10v-45=12 equation:


Simplifying
3v2 + 10v + -45 = 12

Reorder the terms:
-45 + 10v + 3v2 = 12

Solving
-45 + 10v + 3v2 = 12

Solving for variable 'v'.

Reorder the terms:
-45 + -12 + 10v + 3v2 = 12 + -12

Combine like terms: -45 + -12 = -57
-57 + 10v + 3v2 = 12 + -12

Combine like terms: 12 + -12 = 0
-57 + 10v + 3v2 = 0

Factor a trinomial.
(-19 + -3v)(3 + -1v) = 0

Subproblem 1

Set the factor '(-19 + -3v)' equal to zero and attempt to solve: Simplifying -19 + -3v = 0 Solving -19 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -3v = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -3v = 0 + 19 -3v = 0 + 19 Combine like terms: 0 + 19 = 19 -3v = 19 Divide each side by '-3'. v = -6.333333333 Simplifying v = -6.333333333

Subproblem 2

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

Solution

v = {-6.333333333, 3}

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