4t^2-14t=6t-21

Solution for 4t^2-14t=6t-21 equation:

Simplifying
4t2 + -14t = 6t + -21

Reorder the terms:
-14t + 4t2 = 6t + -21

Reorder the terms:
-14t + 4t2 = -21 + 6t

Solving
-14t + 4t2 = -21 + 6t

Solving for variable 't'.

Reorder the terms:
21 + -14t + -6t + 4t2 = -21 + 6t + 21 + -6t

Combine like terms: -14t + -6t = -20t
21 + -20t + 4t2 = -21 + 6t + 21 + -6t

Reorder the terms:
21 + -20t + 4t2 = -21 + 21 + 6t + -6t

Combine like terms: -21 + 21 = 0
21 + -20t + 4t2 = 0 + 6t + -6t
21 + -20t + 4t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
21 + -20t + 4t2 = 0

Factor a trinomial.
(3 + -2t)(7 + -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 '(7 + -2t)' equal to zero and attempt to solve:

Simplifying
7 + -2t = 0

Solving
7 + -2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2t = 0 + -7
-2t = 0 + -7

Combine like terms: 0 + -7 = -7
-2t = -7

Divide each side by '-2'.
t = 3.5

Simplifying
t = 3.5
Solution
t = {1.5, 3.5}