(5t-3)(5t-3)=(4t-1)(4t-1)

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Solution for (5t-3)(5t-3)=(4t-1)(4t-1) equation: 


Simplifying
(5t + -3)(5t + -3) = (4t + -1)(4t + -1)

Reorder the terms:
(-3 + 5t)(5t + -3) = (4t + -1)(4t + -1)

Reorder the terms:
(-3 + 5t)(-3 + 5t) = (4t + -1)(4t + -1)

Multiply (-3 + 5t) * (-3 + 5t)
(-3(-3 + 5t) + 5t * (-3 + 5t)) = (4t + -1)(4t + -1)
((-3 * -3 + 5t * -3) + 5t * (-3 + 5t)) = (4t + -1)(4t + -1)
((9 + -15t) + 5t * (-3 + 5t)) = (4t + -1)(4t + -1)
(9 + -15t + (-3 * 5t + 5t * 5t)) = (4t + -1)(4t + -1)
(9 + -15t + (-15t + 25t2)) = (4t + -1)(4t + -1)

Combine like terms: -15t + -15t = -30t
(9 + -30t + 25t2) = (4t + -1)(4t + -1)

Reorder the terms:
9 + -30t + 25t2 = (-1 + 4t)(4t + -1)

Reorder the terms:
9 + -30t + 25t2 = (-1 + 4t)(-1 + 4t)

Multiply (-1 + 4t) * (-1 + 4t)
9 + -30t + 25t2 = (-1(-1 + 4t) + 4t * (-1 + 4t))
9 + -30t + 25t2 = ((-1 * -1 + 4t * -1) + 4t * (-1 + 4t))
9 + -30t + 25t2 = ((1 + -4t) + 4t * (-1 + 4t))
9 + -30t + 25t2 = (1 + -4t + (-1 * 4t + 4t * 4t))
9 + -30t + 25t2 = (1 + -4t + (-4t + 16t2))

Combine like terms: -4t + -4t = -8t
9 + -30t + 25t2 = (1 + -8t + 16t2)

Solving
9 + -30t + 25t2 = 1 + -8t + 16t2

Solving for variable 't'.

Reorder the terms:
9 + -1 + -30t + 8t + 25t2 + -16t2 = 1 + -8t + 16t2 + -1 + 8t + -16t2

Combine like terms: 9 + -1 = 8
8 + -30t + 8t + 25t2 + -16t2 = 1 + -8t + 16t2 + -1 + 8t + -16t2

Combine like terms: -30t + 8t = -22t
8 + -22t + 25t2 + -16t2 = 1 + -8t + 16t2 + -1 + 8t + -16t2

Combine like terms: 25t2 + -16t2 = 9t2
8 + -22t + 9t2 = 1 + -8t + 16t2 + -1 + 8t + -16t2

Reorder the terms:
8 + -22t + 9t2 = 1 + -1 + -8t + 8t + 16t2 + -16t2

Combine like terms: 1 + -1 = 0
8 + -22t + 9t2 = 0 + -8t + 8t + 16t2 + -16t2
8 + -22t + 9t2 = -8t + 8t + 16t2 + -16t2

Combine like terms: -8t + 8t = 0
8 + -22t + 9t2 = 0 + 16t2 + -16t2
8 + -22t + 9t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
8 + -22t + 9t2 = 0

Factor a trinomial.
(4 + -9t)(2 + -1t) = 0


Subproblem 1
Set the factor '(4 + -9t)' equal to zero and attempt to solve:

Simplifying
4 + -9t = 0

Solving
4 + -9t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9t = 0 + -4
-9t = 0 + -4

Combine like terms: 0 + -4 = -4
-9t = -4

Divide each side by '-9'.
t = 0.4444444444

Simplifying
t = 0.4444444444

Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.4444444444, 2}

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