4t^2=-6t

Solution for 4t^2=-6t equation:

Simplifying
4t2 = -6t

Solving
4t2 = -6t

Solving for variable 't'.

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

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

Factor out the Greatest Common Factor (GCF), '2t'.
2t(3 + 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 '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {0, -1.5}