-1(v-4)=-4(v-1)(v-4)-5(v-1)

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Solution for -1(v-4)=-4(v-1)(v-4)-5(v-1) equation: 


Simplifying
-1(v + -4) = -4(v + -1)(v + -4) + -5(v + -1)

Reorder the terms:
-1(-4 + v) = -4(v + -1)(v + -4) + -5(v + -1)
(-4 * -1 + v * -1) = -4(v + -1)(v + -4) + -5(v + -1)
(4 + -1v) = -4(v + -1)(v + -4) + -5(v + -1)

Reorder the terms:
4 + -1v = -4(-1 + v)(v + -4) + -5(v + -1)

Reorder the terms:
4 + -1v = -4(-1 + v)(-4 + v) + -5(v + -1)

Multiply (-1 + v) * (-4 + v)
4 + -1v = -4(-1(-4 + v) + v(-4 + v)) + -5(v + -1)
4 + -1v = -4((-4 * -1 + v * -1) + v(-4 + v)) + -5(v + -1)
4 + -1v = -4((4 + -1v) + v(-4 + v)) + -5(v + -1)
4 + -1v = -4(4 + -1v + (-4 * v + v * v)) + -5(v + -1)
4 + -1v = -4(4 + -1v + (-4v + v2)) + -5(v + -1)

Combine like terms: -1v + -4v = -5v
4 + -1v = -4(4 + -5v + v2) + -5(v + -1)
4 + -1v = (4 * -4 + -5v * -4 + v2 * -4) + -5(v + -1)
4 + -1v = (-16 + 20v + -4v2) + -5(v + -1)

Reorder the terms:
4 + -1v = -16 + 20v + -4v2 + -5(-1 + v)
4 + -1v = -16 + 20v + -4v2 + (-1 * -5 + v * -5)
4 + -1v = -16 + 20v + -4v2 + (5 + -5v)

Reorder the terms:
4 + -1v = -16 + 5 + 20v + -5v + -4v2

Combine like terms: -16 + 5 = -11
4 + -1v = -11 + 20v + -5v + -4v2

Combine like terms: 20v + -5v = 15v
4 + -1v = -11 + 15v + -4v2

Solving
4 + -1v = -11 + 15v + -4v2

Solving for variable 'v'.

Reorder the terms:
4 + 11 + -1v + -15v + 4v2 = -11 + 15v + -4v2 + 11 + -15v + 4v2

Combine like terms: 4 + 11 = 15
15 + -1v + -15v + 4v2 = -11 + 15v + -4v2 + 11 + -15v + 4v2

Combine like terms: -1v + -15v = -16v
15 + -16v + 4v2 = -11 + 15v + -4v2 + 11 + -15v + 4v2

Reorder the terms:
15 + -16v + 4v2 = -11 + 11 + 15v + -15v + -4v2 + 4v2

Combine like terms: -11 + 11 = 0
15 + -16v + 4v2 = 0 + 15v + -15v + -4v2 + 4v2
15 + -16v + 4v2 = 15v + -15v + -4v2 + 4v2

Combine like terms: 15v + -15v = 0
15 + -16v + 4v2 = 0 + -4v2 + 4v2
15 + -16v + 4v2 = -4v2 + 4v2

Combine like terms: -4v2 + 4v2 = 0
15 + -16v + 4v2 = 0

Factor a trinomial.
(3 + -2v)(5 + -2v) = 0


Subproblem 1
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 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 + -2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2v = 0 + -3
-2v = 0 + -3

Combine like terms: 0 + -3 = -3
-2v = -3

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5

Subproblem 2
Set the factor '(5 + -2v)' equal to zero and attempt to solve:

Simplifying
5 + -2v = 0

Solving
5 + -2v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2v = 0 + -5
-2v = 0 + -5

Combine like terms: 0 + -5 = -5
-2v = -5

Divide each side by '-2'.
v = 2.5

Simplifying
v = 2.5
Solution
v = {1.5, 2.5}

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