(5t-3)(t-2)=3t^2-4t+2

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Solution for (5t-3)(t-2)=3t^2-4t+2 equation: 


Simplifying
(5t + -3)(t + -2) = 3t2 + -4t + 2

Reorder the terms:
(-3 + 5t)(t + -2) = 3t2 + -4t + 2

Reorder the terms:
(-3 + 5t)(-2 + t) = 3t2 + -4t + 2

Multiply (-3 + 5t) * (-2 + t)
(-3(-2 + t) + 5t * (-2 + t)) = 3t2 + -4t + 2
((-2 * -3 + t * -3) + 5t * (-2 + t)) = 3t2 + -4t + 2
((6 + -3t) + 5t * (-2 + t)) = 3t2 + -4t + 2
(6 + -3t + (-2 * 5t + t * 5t)) = 3t2 + -4t + 2
(6 + -3t + (-10t + 5t2)) = 3t2 + -4t + 2

Combine like terms: -3t + -10t = -13t
(6 + -13t + 5t2) = 3t2 + -4t + 2

Reorder the terms:
6 + -13t + 5t2 = 2 + -4t + 3t2

Solving
6 + -13t + 5t2 = 2 + -4t + 3t2

Solving for variable 't'.

Reorder the terms:
6 + -2 + -13t + 4t + 5t2 + -3t2 = 2 + -4t + 3t2 + -2 + 4t + -3t2

Combine like terms: 6 + -2 = 4
4 + -13t + 4t + 5t2 + -3t2 = 2 + -4t + 3t2 + -2 + 4t + -3t2

Combine like terms: -13t + 4t = -9t
4 + -9t + 5t2 + -3t2 = 2 + -4t + 3t2 + -2 + 4t + -3t2

Combine like terms: 5t2 + -3t2 = 2t2
4 + -9t + 2t2 = 2 + -4t + 3t2 + -2 + 4t + -3t2

Reorder the terms:
4 + -9t + 2t2 = 2 + -2 + -4t + 4t + 3t2 + -3t2

Combine like terms: 2 + -2 = 0
4 + -9t + 2t2 = 0 + -4t + 4t + 3t2 + -3t2
4 + -9t + 2t2 = -4t + 4t + 3t2 + -3t2

Combine like terms: -4t + 4t = 0
4 + -9t + 2t2 = 0 + 3t2 + -3t2
4 + -9t + 2t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
4 + -9t + 2t2 = 0

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


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

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

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

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5

Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 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 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {0.5, 4}

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