(4v-7)(6v+8)v=

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Solution for (4v-7)(6v+8)v= equation: 


Simplifying
(4v + -7)(6v + 8) * v = 0

Reorder the terms:
(-7 + 4v)(6v + 8) * v = 0

Reorder the terms:
(-7 + 4v)(8 + 6v) * v = 0

Reorder the terms for easier multiplication:
v(-7 + 4v)(8 + 6v) = 0

Multiply (-7 + 4v) * (8 + 6v)
v(-7(8 + 6v) + 4v * (8 + 6v)) = 0
v((8 * -7 + 6v * -7) + 4v * (8 + 6v)) = 0
v((-56 + -42v) + 4v * (8 + 6v)) = 0
v(-56 + -42v + (8 * 4v + 6v * 4v)) = 0
v(-56 + -42v + (32v + 24v2)) = 0

Combine like terms: -42v + 32v = -10v
v(-56 + -10v + 24v2) = 0
(-56 * v + -10v * v + 24v2 * v) = 0
(-56v + -10v2 + 24v3) = 0

Solving
-56v + -10v2 + 24v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2v'.
2v(-28 + -5v + 12v2) = 0

Factor a trinomial.
2v((-4 + -3v)(7 + -4v)) = 0

Ignore the factor 2.

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 '(-4 + -3v)' equal to zero and attempt to solve:

Simplifying
-4 + -3v = 0

Solving
-4 + -3v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3v = 0 + 4
-3v = 0 + 4

Combine like terms: 0 + 4 = 4
-3v = 4

Divide each side by '-3'.
v = -1.333333333

Simplifying
v = -1.333333333

Subproblem 3
Set the factor '(7 + -4v)' equal to zero and attempt to solve:

Simplifying
7 + -4v = 0

Solving
7 + -4v = 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 + -4v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4v = 0 + -7
-4v = 0 + -7

Combine like terms: 0 + -7 = -7
-4v = -7

Divide each side by '-4'.
v = 1.75

Simplifying
v = 1.75
Solution
v = {0, -1.333333333, 1.75}

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