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

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


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

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

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

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

Combine like terms: -15t + -15t = -30t
(9 + -30t + 25t2) = (4t + -1)(5t + -3)

Reorder the terms:
9 + -30t + 25t2 = (-1 + 4t)(5t + -3)

Reorder the terms:
9 + -30t + 25t2 = (-1 + 4t)(-3 + 5t)

Multiply (-1 + 4t) * (-3 + 5t)
9 + -30t + 25t2 = (-1(-3 + 5t) + 4t * (-3 + 5t))
9 + -30t + 25t2 = ((-3 * -1 + 5t * -1) + 4t * (-3 + 5t))
9 + -30t + 25t2 = ((3 + -5t) + 4t * (-3 + 5t))
9 + -30t + 25t2 = (3 + -5t + (-3 * 4t + 5t * 4t))
9 + -30t + 25t2 = (3 + -5t + (-12t + 20t2))

Combine like terms: -5t + -12t = -17t
9 + -30t + 25t2 = (3 + -17t + 20t2)

Solving
9 + -30t + 25t2 = 3 + -17t + 20t2

Solving for variable 't'.

Reorder the terms:
9 + -3 + -30t + 17t + 25t2 + -20t2 = 3 + -17t + 20t2 + -3 + 17t + -20t2

Combine like terms: 9 + -3 = 6
6 + -30t + 17t + 25t2 + -20t2 = 3 + -17t + 20t2 + -3 + 17t + -20t2

Combine like terms: -30t + 17t = -13t
6 + -13t + 25t2 + -20t2 = 3 + -17t + 20t2 + -3 + 17t + -20t2

Combine like terms: 25t2 + -20t2 = 5t2
6 + -13t + 5t2 = 3 + -17t + 20t2 + -3 + 17t + -20t2

Reorder the terms:
6 + -13t + 5t2 = 3 + -3 + -17t + 17t + 20t2 + -20t2

Combine like terms: 3 + -3 = 0
6 + -13t + 5t2 = 0 + -17t + 17t + 20t2 + -20t2
6 + -13t + 5t2 = -17t + 17t + 20t2 + -20t2

Combine like terms: -17t + 17t = 0
6 + -13t + 5t2 = 0 + 20t2 + -20t2
6 + -13t + 5t2 = 20t2 + -20t2

Combine like terms: 20t2 + -20t2 = 0
6 + -13t + 5t2 = 0

Factor a trinomial.
(3 + -5t)(2 + -1t) = 0


Subproblem 1
Set the factor '(3 + -5t)' equal to zero and attempt to solve:

Simplifying
3 + -5t = 0

Solving
3 + -5t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5t = 0 + -3
-5t = 0 + -3

Combine like terms: 0 + -3 = -3
-5t = -3

Divide each side by '-5'.
t = 0.6

Simplifying
t = 0.6

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 = {0.6, 2}

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