t(6t-14)=-4

Solution for t(6t-14)=-4 equation:

Simplifying
t(6t + -14) = -4

Reorder the terms:
t(-14 + 6t) = -4
(-14 * t + 6t * t) = -4
(-14t + 6t2) = -4

Solving
-14t + 6t2 = -4

Solving for variable 't'.

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

Combine like terms: -4 + 4 = 0
4 + -14t + 6t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -7t + 3t2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 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 + -3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3t = 0 + -1
-3t = 0 + -1

Combine like terms: 0 + -1 = -1
-3t = -1

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.3333333333, 2}