(4t-5)(t+6)=-51

Solution for (4t-5)(t+6)=-51 equation:

Simplifying
(4t + -5)(t + 6) = -51

Reorder the terms:
(-5 + 4t)(t + 6) = -51

Reorder the terms:
(-5 + 4t)(6 + t) = -51

Multiply (-5 + 4t) * (6 + t)
(-5(6 + t) + 4t * (6 + t)) = -51
((6 * -5 + t * -5) + 4t * (6 + t)) = -51
((-30 + -5t) + 4t * (6 + t)) = -51
(-30 + -5t + (6 * 4t + t * 4t)) = -51
(-30 + -5t + (24t + 4t2)) = -51

Combine like terms: -5t + 24t = 19t
(-30 + 19t + 4t2) = -51

Solving
-30 + 19t + 4t2 = -51

Solving for variable 't'.

Reorder the terms:
-30 + 51 + 19t + 4t2 = -51 + 51

Combine like terms: -30 + 51 = 21
21 + 19t + 4t2 = -51 + 51

Combine like terms: -51 + 51 = 0
21 + 19t + 4t2 = 0

Factor a trinomial.
(3 + t)(7 + 4t) = 0

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

Simplifying
3 + t = 0

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

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

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

Simplifying
t = -3
Subproblem 2
Set the factor '(7 + 4t)' equal to zero and attempt to solve:

Simplifying
7 + 4t = 0

Solving
7 + 4t = 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 + 4t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4t = 0 + -7
4t = 0 + -7

Combine like terms: 0 + -7 = -7
4t = -7

Divide each side by '4'.
t = -1.75

Simplifying
t = -1.75
Solution
t = {-3, -1.75}