(7t+3)(4t-2)=

Solution for (7t+3)(4t-2)= equation:

Simplifying
(7t + 3)(4t + -2) = 0

Reorder the terms:
(3 + 7t)(4t + -2) = 0

Reorder the terms:
(3 + 7t)(-2 + 4t) = 0

Multiply (3 + 7t) * (-2 + 4t)
(3(-2 + 4t) + 7t * (-2 + 4t)) = 0
((-2 * 3 + 4t * 3) + 7t * (-2 + 4t)) = 0
((-6 + 12t) + 7t * (-2 + 4t)) = 0
(-6 + 12t + (-2 * 7t + 4t * 7t)) = 0
(-6 + 12t + (-14t + 28t2)) = 0

Combine like terms: 12t + -14t = -2t
(-6 + -2t + 28t2) = 0

Solving
-6 + -2t + 28t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1t + 14t2) = 0

Factor a trinomial.
2((-3 + -7t)(1 + -2t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -7t)' equal to zero and attempt to solve:

Simplifying
-3 + -7t = 0

Solving
-3 + -7t = 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 + -7t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7t = 0 + 3
-7t = 0 + 3

Combine like terms: 0 + 3 = 3
-7t = 3

Divide each side by '-7'.
t = -0.4285714286

Simplifying
t = -0.4285714286
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 = {-0.4285714286, 0.5}