(t+4)(2t-10)=0

Solution for (t+4)(2t-10)=0 equation:

Simplifying
(t + 4)(2t + -10) = 0

Reorder the terms:
(4 + t)(2t + -10) = 0

Reorder the terms:
(4 + t)(-10 + 2t) = 0

Multiply (4 + t) * (-10 + 2t)
(4(-10 + 2t) + t(-10 + 2t)) = 0
((-10 * 4 + 2t * 4) + t(-10 + 2t)) = 0
((-40 + 8t) + t(-10 + 2t)) = 0
(-40 + 8t + (-10 * t + 2t * t)) = 0
(-40 + 8t + (-10t + 2t2)) = 0

Combine like terms: 8t + -10t = -2t
(-40 + -2t + 2t2) = 0

Solving
-40 + -2t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -1t + t2) = 0

Factor a trinomial.
2((-4 + -1t)(5 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 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 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-4, 5}