4t^2+2t+9=14t

Solution for 4t^2+2t+9=14t equation:

Simplifying
4t2 + 2t + 9 = 14t

Reorder the terms:
9 + 2t + 4t2 = 14t

Solving
9 + 2t + 4t2 = 14t

Solving for variable 't'.

Reorder the terms:
9 + 2t + -14t + 4t2 = 14t + -14t

Combine like terms: 2t + -14t = -12t
9 + -12t + 4t2 = 14t + -14t

Combine like terms: 14t + -14t = 0
9 + -12t + 4t2 = 0

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

Subproblem 1
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
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 = {1.5, 1.5}