7v^2(v^2+v-2)=0

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Solution for 7v^2(v^2+v-2)=0 equation: 


Simplifying
7v2(v2 + v + -2) = 0

Reorder the terms:
7v2(-2 + v + v2) = 0
(-2 * 7v2 + v * 7v2 + v2 * 7v2) = 0
(-14v2 + 7v3 + 7v4) = 0

Solving
-14v2 + 7v3 + 7v4 = 0

Solving for variable 'v'.

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

Factor a trinomial.
7v2((-2 + -1v)(1 + -1v)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

Move all terms containing v to the left, all other terms to the right.

Simplifying
v2 = 0

Take the square root of each side:
v = {0}

Subproblem 2
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 3
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1v = 0 + -1
-1v = 0 + -1

Combine like terms: 0 + -1 = -1
-1v = -1

Divide each side by '-1'.
v = 1

Simplifying
v = 1
Solution
v = {0, -2, 1}

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