(7-v)(4v-2)=0

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Solution for (7-v)(4v-2)=0 equation: 


Simplifying
(7 + -1v)(4v + -2) = 0

Reorder the terms:
(7 + -1v)(-2 + 4v) = 0

Multiply (7 + -1v) * (-2 + 4v)
(7(-2 + 4v) + -1v * (-2 + 4v)) = 0
((-2 * 7 + 4v * 7) + -1v * (-2 + 4v)) = 0
((-14 + 28v) + -1v * (-2 + 4v)) = 0
(-14 + 28v + (-2 * -1v + 4v * -1v)) = 0
(-14 + 28v + (2v + -4v2)) = 0

Combine like terms: 28v + 2v = 30v
(-14 + 30v + -4v2) = 0

Solving
-14 + 30v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 15v + -2v2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + v)' equal to zero and attempt to solve:

Simplifying
-7 + v = 0

Solving
-7 + v = 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 + v = 0 + 7

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

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

Simplifying
v = 7

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

Simplifying
1 + -2v = 0

Solving
1 + -2v = 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 + -2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2v = 0 + -1
-2v = 0 + -1

Combine like terms: 0 + -1 = -1
-2v = -1

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5
Solution
v = {7, 0.5}

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