0=v^2+7v+10

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Solution for 0=v^2+7v+10 equation:


Simplifying
0 = v2 + 7v + 10

Reorder the terms:
0 = 10 + 7v + v2

Solving
0 = 10 + 7v + v2

Solving for variable 'v'.

Combine like terms: 0 + -10 = -10
-10 + -7v + -1v2 = 10 + 7v + v2 + -10 + -7v + -1v2

Reorder the terms:
-10 + -7v + -1v2 = 10 + -10 + 7v + -7v + v2 + -1v2

Combine like terms: 10 + -10 = 0
-10 + -7v + -1v2 = 0 + 7v + -7v + v2 + -1v2
-10 + -7v + -1v2 = 7v + -7v + v2 + -1v2

Combine like terms: 7v + -7v = 0
-10 + -7v + -1v2 = 0 + v2 + -1v2
-10 + -7v + -1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-10 + -7v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 7v + v2) = 0

Factor a trinomial.
-1((5 + v)(2 + v)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5

Subproblem 2

Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 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 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2

Solution

v = {-5, -2}

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