t(t-2)+2(2t-1)=t+4

Solution for t(t-2)+2(2t-1)=t+4 equation:

Simplifying
t(t + -2) + 2(2t + -1) = t + 4

Reorder the terms:
t(-2 + t) + 2(2t + -1) = t + 4
(-2 * t + t * t) + 2(2t + -1) = t + 4
(-2t + t2) + 2(2t + -1) = t + 4

Reorder the terms:
-2t + t2 + 2(-1 + 2t) = t + 4
-2t + t2 + (-1 * 2 + 2t * 2) = t + 4
-2t + t2 + (-2 + 4t) = t + 4

Reorder the terms:
-2 + -2t + 4t + t2 = t + 4

Combine like terms: -2t + 4t = 2t
-2 + 2t + t2 = t + 4

Reorder the terms:
-2 + 2t + t2 = 4 + t

Solving
-2 + 2t + t2 = 4 + t

Solving for variable 't'.

Reorder the terms:
-2 + -4 + 2t + -1t + t2 = 4 + t + -4 + -1t

Combine like terms: -2 + -4 = -6
-6 + 2t + -1t + t2 = 4 + t + -4 + -1t

Combine like terms: 2t + -1t = 1t
-6 + 1t + t2 = 4 + t + -4 + -1t

Reorder the terms:
-6 + 1t + t2 = 4 + -4 + t + -1t

Combine like terms: 4 + -4 = 0
-6 + 1t + t2 = 0 + t + -1t
-6 + 1t + t2 = t + -1t

Combine like terms: t + -1t = 0
-6 + 1t + t2 = 0

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

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
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 = {-3, 2}