4t(t-5)=2t

Solution for 4t(t-5)=2t equation:

Simplifying
4t(t + -5) = 2t

Reorder the terms:
4t(-5 + t) = 2t
(-5 * 4t + t * 4t) = 2t
(-20t + 4t2) = 2t

Solving
-20t + 4t2 = 2t

Solving for variable 't'.

Reorder the terms:
-20t + -2t + 4t2 = 2t + -2t

Combine like terms: -20t + -2t = -22t
-22t + 4t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-22t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2t'.
2t(-11 + 2t) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-11 + 2t)' equal to zero and attempt to solve:

Simplifying
-11 + 2t = 0

Solving
-11 + 2t = 0

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

Add '11' to each side of the equation.
-11 + 11 + 2t = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2t = 0 + 11
2t = 0 + 11

Combine like terms: 0 + 11 = 11
2t = 11

Divide each side by '2'.
t = 5.5

Simplifying
t = 5.5
Solution
t = {0, 5.5}