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

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


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

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

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

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

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

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

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

Solving for variable 'v'.

Reorder the terms:
-3 + -9 + 7v + -6v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: -3 + -9 = -12
-12 + 7v + -6v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: 7v + -6v = 1v
-12 + 1v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-12 + 1v + 1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Reorder the terms:
-12 + 1v + 1v2 = 9 + -9 + 6v + -6v + v2 + -1v2

Combine like terms: 9 + -9 = 0
-12 + 1v + 1v2 = 0 + 6v + -6v + v2 + -1v2
-12 + 1v + 1v2 = 6v + -6v + v2 + -1v2

Combine like terms: 6v + -6v = 0
-12 + 1v + 1v2 = 0 + v2 + -1v2
-12 + 1v + 1v2 = v2 + -1v2

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

Factor a trinomial.
(-4 + -1v)(3 + -1v) = 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 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

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

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