t^2+3t-10=4+8t

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Solution for t^2+3t-10=4+8t equation: 


Simplifying
t2 + 3t + -10 = 4 + 8t

Reorder the terms:
-10 + 3t + t2 = 4 + 8t

Solving
-10 + 3t + t2 = 4 + 8t

Solving for variable 't'.

Reorder the terms:
-10 + -4 + 3t + -8t + t2 = 4 + 8t + -4 + -8t

Combine like terms: -10 + -4 = -14
-14 + 3t + -8t + t2 = 4 + 8t + -4 + -8t

Combine like terms: 3t + -8t = -5t
-14 + -5t + t2 = 4 + 8t + -4 + -8t

Reorder the terms:
-14 + -5t + t2 = 4 + -4 + 8t + -8t

Combine like terms: 4 + -4 = 0
-14 + -5t + t2 = 0 + 8t + -8t
-14 + -5t + t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
-14 + -5t + t2 = 0

Factor a trinomial.
(-2 + -1t)(7 + -1t) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-2, 7}

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