t^2-20t+125=4t-10

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Solution for t^2-20t+125=4t-10 equation: 


Simplifying
t2 + -20t + 125 = 4t + -10

Reorder the terms:
125 + -20t + t2 = 4t + -10

Reorder the terms:
125 + -20t + t2 = -10 + 4t

Solving
125 + -20t + t2 = -10 + 4t

Solving for variable 't'.

Reorder the terms:
125 + 10 + -20t + -4t + t2 = -10 + 4t + 10 + -4t

Combine like terms: 125 + 10 = 135
135 + -20t + -4t + t2 = -10 + 4t + 10 + -4t

Combine like terms: -20t + -4t = -24t
135 + -24t + t2 = -10 + 4t + 10 + -4t

Reorder the terms:
135 + -24t + t2 = -10 + 10 + 4t + -4t

Combine like terms: -10 + 10 = 0
135 + -24t + t2 = 0 + 4t + -4t
135 + -24t + t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
135 + -24t + t2 = 0

Factor a trinomial.
(9 + -1t)(15 + -1t) = 0


Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9

Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve:

Simplifying
15 + -1t = 0

Solving
15 + -1t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1t = 0 + -15
-1t = 0 + -15

Combine like terms: 0 + -15 = -15
-1t = -15

Divide each side by '-1'.
t = 15

Simplifying
t = 15
Solution
t = {9, 15}

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