3t^2-4t=6t-8

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Solution for 3t^2-4t=6t-8 equation: 


Simplifying
3t2 + -4t = 6t + -8

Reorder the terms:
-4t + 3t2 = 6t + -8

Reorder the terms:
-4t + 3t2 = -8 + 6t

Solving
-4t + 3t2 = -8 + 6t

Solving for variable 't'.

Reorder the terms:
8 + -4t + -6t + 3t2 = -8 + 6t + 8 + -6t

Combine like terms: -4t + -6t = -10t
8 + -10t + 3t2 = -8 + 6t + 8 + -6t

Reorder the terms:
8 + -10t + 3t2 = -8 + 8 + 6t + -6t

Combine like terms: -8 + 8 = 0
8 + -10t + 3t2 = 0 + 6t + -6t
8 + -10t + 3t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
8 + -10t + 3t2 = 0

Factor a trinomial.
(4 + -3t)(2 + -1t) = 0


Subproblem 1
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 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 + -3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3t = 0 + -4
-3t = 0 + -4

Combine like terms: 0 + -4 = -4
-3t = -4

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333

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 = {1.333333333, 2}

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