2v^2-10v+13=(v-1)(v-1)

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Solution for 2v^2-10v+13=(v-1)(v-1) equation: 


Simplifying
2v2 + -10v + 13 = (v + -1)(v + -1)

Reorder the terms:
13 + -10v + 2v2 = (v + -1)(v + -1)

Reorder the terms:
13 + -10v + 2v2 = (-1 + v)(v + -1)

Reorder the terms:
13 + -10v + 2v2 = (-1 + v)(-1 + v)

Multiply (-1 + v) * (-1 + v)
13 + -10v + 2v2 = (-1(-1 + v) + v(-1 + v))
13 + -10v + 2v2 = ((-1 * -1 + v * -1) + v(-1 + v))
13 + -10v + 2v2 = ((1 + -1v) + v(-1 + v))
13 + -10v + 2v2 = (1 + -1v + (-1 * v + v * v))
13 + -10v + 2v2 = (1 + -1v + (-1v + v2))

Combine like terms: -1v + -1v = -2v
13 + -10v + 2v2 = (1 + -2v + v2)

Solving
13 + -10v + 2v2 = 1 + -2v + v2

Solving for variable 'v'.

Reorder the terms:
13 + -1 + -10v + 2v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: 13 + -1 = 12
12 + -10v + 2v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: -10v + 2v = -8v
12 + -8v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
12 + -8v + 1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Reorder the terms:
12 + -8v + 1v2 = 1 + -1 + -2v + 2v + v2 + -1v2

Combine like terms: 1 + -1 = 0
12 + -8v + 1v2 = 0 + -2v + 2v + v2 + -1v2
12 + -8v + 1v2 = -2v + 2v + v2 + -1v2

Combine like terms: -2v + 2v = 0
12 + -8v + 1v2 = 0 + v2 + -1v2
12 + -8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
12 + -8v + 1v2 = 0

Factor a trinomial.
(2 + -1v)(6 + -1v) = 0


Subproblem 1
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 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {2, 6}

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