50t+275=3t^2+70t+100

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Solution for 50t+275=3t^2+70t+100 equation: 


Simplifying
50t + 275 = 3t2 + 70t + 100

Reorder the terms:
275 + 50t = 3t2 + 70t + 100

Reorder the terms:
275 + 50t = 100 + 70t + 3t2

Solving
275 + 50t = 100 + 70t + 3t2

Solving for variable 't'.

Reorder the terms:
275 + -100 + 50t + -70t + -3t2 = 100 + 70t + 3t2 + -100 + -70t + -3t2

Combine like terms: 275 + -100 = 175
175 + 50t + -70t + -3t2 = 100 + 70t + 3t2 + -100 + -70t + -3t2

Combine like terms: 50t + -70t = -20t
175 + -20t + -3t2 = 100 + 70t + 3t2 + -100 + -70t + -3t2

Reorder the terms:
175 + -20t + -3t2 = 100 + -100 + 70t + -70t + 3t2 + -3t2

Combine like terms: 100 + -100 = 0
175 + -20t + -3t2 = 0 + 70t + -70t + 3t2 + -3t2
175 + -20t + -3t2 = 70t + -70t + 3t2 + -3t2

Combine like terms: 70t + -70t = 0
175 + -20t + -3t2 = 0 + 3t2 + -3t2
175 + -20t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
175 + -20t + -3t2 = 0

Factor a trinomial.
(5 + -1t)(35 + 3t) = 0


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

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5

Subproblem 2
Set the factor '(35 + 3t)' equal to zero and attempt to solve:

Simplifying
35 + 3t = 0

Solving
35 + 3t = 0

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

Add '-35' to each side of the equation.
35 + -35 + 3t = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 3t = 0 + -35
3t = 0 + -35

Combine like terms: 0 + -35 = -35
3t = -35

Divide each side by '3'.
t = -11.66666667

Simplifying
t = -11.66666667
Solution
t = {5, -11.66666667}

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