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

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


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

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

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

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

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

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

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

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

Combine like terms: -20w + -1w = -21w
20 + -21w + 4w2 = -5(w + -1)

Reorder the terms:
20 + -21w + 4w2 = -5(-1 + w)
20 + -21w + 4w2 = (-1 * -5 + w * -5)
20 + -21w + 4w2 = (5 + -5w)

Solving
20 + -21w + 4w2 = 5 + -5w

Solving for variable 'w'.

Reorder the terms:
20 + -5 + -21w + 5w + 4w2 = 5 + -5w + -5 + 5w

Combine like terms: 20 + -5 = 15
15 + -21w + 5w + 4w2 = 5 + -5w + -5 + 5w

Combine like terms: -21w + 5w = -16w
15 + -16w + 4w2 = 5 + -5w + -5 + 5w

Reorder the terms:
15 + -16w + 4w2 = 5 + -5 + -5w + 5w

Combine like terms: 5 + -5 = 0
15 + -16w + 4w2 = 0 + -5w + 5w
15 + -16w + 4w2 = -5w + 5w

Combine like terms: -5w + 5w = 0
15 + -16w + 4w2 = 0

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


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

Simplifying
3 + -2w = 0

Solving
3 + -2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2w = 0 + -3

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

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

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

Simplifying
w = 1.5

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

Simplifying
5 + -2w = 0

Solving
5 + -2w = 0

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

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

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

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

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

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

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