(6t-7)(t+2)=-10

Solution for (6t-7)(t+2)=-10 equation:

Simplifying
(6t + -7)(t + 2) = -10

Reorder the terms:
(-7 + 6t)(t + 2) = -10

Reorder the terms:
(-7 + 6t)(2 + t) = -10

Multiply (-7 + 6t) * (2 + t)
(-7(2 + t) + 6t * (2 + t)) = -10
((2 * -7 + t * -7) + 6t * (2 + t)) = -10
((-14 + -7t) + 6t * (2 + t)) = -10
(-14 + -7t + (2 * 6t + t * 6t)) = -10
(-14 + -7t + (12t + 6t2)) = -10

Combine like terms: -7t + 12t = 5t
(-14 + 5t + 6t2) = -10

Solving
-14 + 5t + 6t2 = -10

Solving for variable 't'.

Reorder the terms:
-14 + 10 + 5t + 6t2 = -10 + 10

Combine like terms: -14 + 10 = -4
-4 + 5t + 6t2 = -10 + 10

Combine like terms: -10 + 10 = 0
-4 + 5t + 6t2 = 0

Factor a trinomial.
(-4 + -3t)(1 + -2t) = 0

Subproblem 1
Set the factor '(-4 + -3t)' equal to zero and attempt to solve:

Simplifying
-4 + -3t = 0

Solving
-4 + -3t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3t = 0 + 4
-3t = 0 + 4

Combine like terms: 0 + 4 = 4
-3t = 4

Divide each side by '-3'.
t = -1.333333333

Simplifying
t = -1.333333333
Subproblem 2
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
Solution
t = {-1.333333333, 0.5}