(t-4)(4)+(t-1)(4)=(5)(t-1)(t-4)

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Solution for (t-4)(4)+(t-1)(4)=(5)(t-1)(t-4) equation: 


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

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

Reorder the terms for easier multiplication:
4(-4 + t) + (t + -1)(4) = (5)(t + -1)(t + -4)
(-4 * 4 + t * 4) + (t + -1)(4) = (5)(t + -1)(t + -4)
(-16 + 4t) + (t + -1)(4) = (5)(t + -1)(t + -4)

Reorder the terms:
-16 + 4t + (-1 + t)(4) = (5)(t + -1)(t + -4)

Reorder the terms for easier multiplication:
-16 + 4t + 4(-1 + t) = (5)(t + -1)(t + -4)
-16 + 4t + (-1 * 4 + t * 4) = (5)(t + -1)(t + -4)
-16 + 4t + (-4 + 4t) = (5)(t + -1)(t + -4)

Reorder the terms:
-16 + -4 + 4t + 4t = (5)(t + -1)(t + -4)

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

Combine like terms: 4t + 4t = 8t
-20 + 8t = (5)(t + -1)(t + -4)

Reorder the terms:
-20 + 8t = 5(-1 + t)(t + -4)

Reorder the terms:
-20 + 8t = 5(-1 + t)(-4 + t)

Multiply (-1 + t) * (-4 + t)
-20 + 8t = 5(-1(-4 + t) + t(-4 + t))
-20 + 8t = 5((-4 * -1 + t * -1) + t(-4 + t))
-20 + 8t = 5((4 + -1t) + t(-4 + t))
-20 + 8t = 5(4 + -1t + (-4 * t + t * t))
-20 + 8t = 5(4 + -1t + (-4t + t2))

Combine like terms: -1t + -4t = -5t
-20 + 8t = 5(4 + -5t + t2)
-20 + 8t = (4 * 5 + -5t * 5 + t2 * 5)
-20 + 8t = (20 + -25t + 5t2)

Solving
-20 + 8t = 20 + -25t + 5t2

Solving for variable 't'.

Reorder the terms:
-20 + -20 + 8t + 25t + -5t2 = 20 + -25t + 5t2 + -20 + 25t + -5t2

Combine like terms: -20 + -20 = -40
-40 + 8t + 25t + -5t2 = 20 + -25t + 5t2 + -20 + 25t + -5t2

Combine like terms: 8t + 25t = 33t
-40 + 33t + -5t2 = 20 + -25t + 5t2 + -20 + 25t + -5t2

Reorder the terms:
-40 + 33t + -5t2 = 20 + -20 + -25t + 25t + 5t2 + -5t2

Combine like terms: 20 + -20 = 0
-40 + 33t + -5t2 = 0 + -25t + 25t + 5t2 + -5t2
-40 + 33t + -5t2 = -25t + 25t + 5t2 + -5t2

Combine like terms: -25t + 25t = 0
-40 + 33t + -5t2 = 0 + 5t2 + -5t2
-40 + 33t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-40 + 33t + -5t2 = 0

Factor a trinomial.
(-5 + t)(8 + -5t) = 0


Subproblem 1
Set the factor '(-5 + t)' equal to zero and attempt to solve:

Simplifying
-5 + t = 0

Solving
-5 + t = 0

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

Add '5' to each side of the equation.
-5 + 5 + t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + t = 0 + 5
t = 0 + 5

Combine like terms: 0 + 5 = 5
t = 5

Simplifying
t = 5

Subproblem 2
Set the factor '(8 + -5t)' equal to zero and attempt to solve:

Simplifying
8 + -5t = 0

Solving
8 + -5t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5t = 0 + -8
-5t = 0 + -8

Combine like terms: 0 + -8 = -8
-5t = -8

Divide each side by '-5'.
t = 1.6

Simplifying
t = 1.6
Solution
t = {5, 1.6}

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