4t^2=6+10t

Solution for 4t^2=6+10t equation:

Simplifying
4t2 = 6 + 10t

Solving
4t2 = 6 + 10t

Solving for variable 't'.

Reorder the terms:
-6 + -10t + 4t2 = 6 + 10t + -6 + -10t

Reorder the terms:
-6 + -10t + 4t2 = 6 + -6 + 10t + -10t

Combine like terms: 6 + -6 = 0
-6 + -10t + 4t2 = 0 + 10t + -10t
-6 + -10t + 4t2 = 10t + -10t

Combine like terms: 10t + -10t = 0
-6 + -10t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5t + 2t2) = 0

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

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

Simplifying
-1 + -2t = 0

Solving
-1 + -2t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2t = 0 + 1
-2t = 0 + 1

Combine like terms: 0 + 1 = 1
-2t = 1

Divide each side by '-2'.
t = -0.5

Simplifying
t = -0.5
Subproblem 2
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
Solution
t = {-0.5, 3}