5v(v-7)(v+2)=0

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Solution for 5v(v-7)(v+2)=0 equation: 


Simplifying
5v(v + -7)(v + 2) = 0

Reorder the terms:
5v(-7 + v)(v + 2) = 0

Reorder the terms:
5v(-7 + v)(2 + v) = 0

Multiply (-7 + v) * (2 + v)
5v(-7(2 + v) + v(2 + v)) = 0
5v((2 * -7 + v * -7) + v(2 + v)) = 0
5v((-14 + -7v) + v(2 + v)) = 0
5v(-14 + -7v + (2 * v + v * v)) = 0
5v(-14 + -7v + (2v + v2)) = 0

Combine like terms: -7v + 2v = -5v
5v(-14 + -5v + v2) = 0
(-14 * 5v + -5v * 5v + v2 * 5v) = 0
(-70v + -25v2 + 5v3) = 0

Solving
-70v + -25v2 + 5v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5v'.
5v(-14 + -5v + v2) = 0

Factor a trinomial.
5v((-2 + -1v)(7 + -1v)) = 0

Ignore the factor 5.

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

Simplifying
v = 0

Solving
v = 0

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

Simplifying
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 '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

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

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

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {0, -2, 7}

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