-(1+2t)(7+2t)=0

Solution for -(1+2t)(7+2t)=0 equation:

Simplifying
-1(1 + 2t)(7 + 2t) = 0

Multiply (1 + 2t) * (7 + 2t)
-1(1(7 + 2t) + 2t * (7 + 2t)) = 0
-1((7 * 1 + 2t * 1) + 2t * (7 + 2t)) = 0
-1((7 + 2t) + 2t * (7 + 2t)) = 0
-1(7 + 2t + (7 * 2t + 2t * 2t)) = 0
-1(7 + 2t + (14t + 4t2)) = 0

Combine like terms: 2t + 14t = 16t
-1(7 + 16t + 4t2) = 0
(7 * -1 + 16t * -1 + 4t2 * -1) = 0
(-7 + -16t + -4t2) = 0

Solving
-7 + -16t + -4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 16t + 4t2) = 0

Factor a trinomial.
-1((7 + 2t)(1 + 2t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

Solving
7 + 2t = 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 + 2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
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 = {-3.5, -0.5}