4(w-4)(w-1)=-5(w-1)

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


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

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

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

Multiply (-4 + w) * (-1 + w)
4(-4(-1 + w) + w(-1 + w)) = -5(w + -1)
4((-1 * -4 + w * -4) + w(-1 + w)) = -5(w + -1)
4((4 + -4w) + w(-1 + w)) = -5(w + -1)
4(4 + -4w + (-1 * w + w * w)) = -5(w + -1)
4(4 + -4w + (-1w + w2)) = -5(w + -1)

Combine like terms: -4w + -1w = -5w
4(4 + -5w + w2) = -5(w + -1)
(4 * 4 + -5w * 4 + w2 * 4) = -5(w + -1)
(16 + -20w + 4w2) = -5(w + -1)

Reorder the terms:
16 + -20w + 4w2 = -5(-1 + w)
16 + -20w + 4w2 = (-1 * -5 + w * -5)
16 + -20w + 4w2 = (5 + -5w)

Solving
16 + -20w + 4w2 = 5 + -5w

Solving for variable 'w'.

Reorder the terms:
16 + -5 + -20w + 5w + 4w2 = 5 + -5w + -5 + 5w

Combine like terms: 16 + -5 = 11
11 + -20w + 5w + 4w2 = 5 + -5w + -5 + 5w

Combine like terms: -20w + 5w = -15w
11 + -15w + 4w2 = 5 + -5w + -5 + 5w

Reorder the terms:
11 + -15w + 4w2 = 5 + -5 + -5w + 5w

Combine like terms: 5 + -5 = 0
11 + -15w + 4w2 = 0 + -5w + 5w
11 + -15w + 4w2 = -5w + 5w

Combine like terms: -5w + 5w = 0
11 + -15w + 4w2 = 0

Factor a trinomial.
(1 + -1w)(11 + -4w) = 0


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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1w = 0 + -1
-1w = 0 + -1

Combine like terms: 0 + -1 = -1
-1w = -1

Divide each side by '-1'.
w = 1

Simplifying
w = 1

Subproblem 2
Set the factor '(11 + -4w)' equal to zero and attempt to solve:

Simplifying
11 + -4w = 0

Solving
11 + -4w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4w = 0 + -11
-4w = 0 + -11

Combine like terms: 0 + -11 = -11
-4w = -11

Divide each side by '-4'.
w = 2.75

Simplifying
w = 2.75
Solution
w = {1, 2.75}

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