5*(-6)+(6-t)*(7+t)=0

Solution for 5*(-6)+(6-t)*(7+t)=0 equation:

Simplifying
5(-6) + (6 + -1t)(7 + t) = 0

Multiply 5 * -6
-30 + (6 + -1t)(7 + t) = 0

Multiply (6 + -1t) * (7 + t)
-30 + (6(7 + t) + -1t * (7 + t)) = 0
-30 + ((7 * 6 + t * 6) + -1t * (7 + t)) = 0
-30 + ((42 + 6t) + -1t * (7 + t)) = 0
-30 + (42 + 6t + (7 * -1t + t * -1t)) = 0
-30 + (42 + 6t + (-7t + -1t2)) = 0

Combine like terms: 6t + -7t = -1t
-30 + (42 + -1t + -1t2) = 0

Combine like terms: -30 + 42 = 12
12 + -1t + -1t2 = 0

Solving
12 + -1t + -1t2 = 0

Solving for variable 't'.

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

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

Simplifying
3 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 3

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

Simplifying
4 + t = 0

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

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

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

Simplifying
t = -4
Solution
t = {3, -4}