2-6t(3-t)=(t-3)5-3

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Solution for 2-6t(3-t)=(t-3)5-3 equation: 


Simplifying
2 + -6t(3 + -1t) = (t + -3) * 5 + -3
2 + (3 * -6t + -1t * -6t) = (t + -3) * 5 + -3
2 + (-18t + 6t2) = (t + -3) * 5 + -3

Reorder the terms:
2 + -18t + 6t2 = (-3 + t) * 5 + -3

Reorder the terms for easier multiplication:
2 + -18t + 6t2 = 5(-3 + t) + -3
2 + -18t + 6t2 = (-3 * 5 + t * 5) + -3
2 + -18t + 6t2 = (-15 + 5t) + -3

Reorder the terms:
2 + -18t + 6t2 = -15 + -3 + 5t

Combine like terms: -15 + -3 = -18
2 + -18t + 6t2 = -18 + 5t

Solving
2 + -18t + 6t2 = -18 + 5t

Solving for variable 't'.

Reorder the terms:
2 + 18 + -18t + -5t + 6t2 = -18 + 5t + 18 + -5t

Combine like terms: 2 + 18 = 20
20 + -18t + -5t + 6t2 = -18 + 5t + 18 + -5t

Combine like terms: -18t + -5t = -23t
20 + -23t + 6t2 = -18 + 5t + 18 + -5t

Reorder the terms:
20 + -23t + 6t2 = -18 + 18 + 5t + -5t

Combine like terms: -18 + 18 = 0
20 + -23t + 6t2 = 0 + 5t + -5t
20 + -23t + 6t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
20 + -23t + 6t2 = 0

Factor a trinomial.
(4 + -3t)(5 + -2t) = 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 '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 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 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {1.333333333, 2.5}

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