(v-3)(v-3)=2v^2-7v-3

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Solution for (v-3)(v-3)=2v^2-7v-3 equation: 


Simplifying
(v + -3)(v + -3) = 2v2 + -7v + -3

Reorder the terms:
(-3 + v)(v + -3) = 2v2 + -7v + -3

Reorder the terms:
(-3 + v)(-3 + v) = 2v2 + -7v + -3

Multiply (-3 + v) * (-3 + v)
(-3(-3 + v) + v(-3 + v)) = 2v2 + -7v + -3
((-3 * -3 + v * -3) + v(-3 + v)) = 2v2 + -7v + -3
((9 + -3v) + v(-3 + v)) = 2v2 + -7v + -3
(9 + -3v + (-3 * v + v * v)) = 2v2 + -7v + -3
(9 + -3v + (-3v + v2)) = 2v2 + -7v + -3

Combine like terms: -3v + -3v = -6v
(9 + -6v + v2) = 2v2 + -7v + -3

Reorder the terms:
9 + -6v + v2 = -3 + -7v + 2v2

Solving
9 + -6v + v2 = -3 + -7v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + 3 + -6v + 7v + v2 + -2v2 = -3 + -7v + 2v2 + 3 + 7v + -2v2

Combine like terms: 9 + 3 = 12
12 + -6v + 7v + v2 + -2v2 = -3 + -7v + 2v2 + 3 + 7v + -2v2

Combine like terms: -6v + 7v = 1v
12 + 1v + v2 + -2v2 = -3 + -7v + 2v2 + 3 + 7v + -2v2

Combine like terms: v2 + -2v2 = -1v2
12 + 1v + -1v2 = -3 + -7v + 2v2 + 3 + 7v + -2v2

Reorder the terms:
12 + 1v + -1v2 = -3 + 3 + -7v + 7v + 2v2 + -2v2

Combine like terms: -3 + 3 = 0
12 + 1v + -1v2 = 0 + -7v + 7v + 2v2 + -2v2
12 + 1v + -1v2 = -7v + 7v + 2v2 + -2v2

Combine like terms: -7v + 7v = 0
12 + 1v + -1v2 = 0 + 2v2 + -2v2
12 + 1v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
12 + 1v + -1v2 = 0

Factor a trinomial.
(4 + -1v)(3 + v) = 0


Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 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 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4

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

Simplifying
3 + v = 0

Solving
3 + v = 0

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

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

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

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

Simplifying
v = -3
Solution
v = {4, -3}

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