(7t+5)(2t-3)=0

Solution for (7t+5)(2t-3)=0 equation:

Simplifying
(7t + 5)(2t + -3) = 0

Reorder the terms:
(5 + 7t)(2t + -3) = 0

Reorder the terms:
(5 + 7t)(-3 + 2t) = 0

Multiply (5 + 7t) * (-3 + 2t)
(5(-3 + 2t) + 7t * (-3 + 2t)) = 0
((-3 * 5 + 2t * 5) + 7t * (-3 + 2t)) = 0
((-15 + 10t) + 7t * (-3 + 2t)) = 0
(-15 + 10t + (-3 * 7t + 2t * 7t)) = 0
(-15 + 10t + (-21t + 14t2)) = 0

Combine like terms: 10t + -21t = -11t
(-15 + -11t + 14t2) = 0

Solving
-15 + -11t + 14t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -7t)(3 + -2t) = 0

Subproblem 1
Set the factor '(-5 + -7t)' equal to zero and attempt to solve:

Simplifying
-5 + -7t = 0

Solving
-5 + -7t = 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 + -7t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7t = 0 + 5
-7t = 0 + 5

Combine like terms: 0 + 5 = 5
-7t = 5

Divide each side by '-7'.
t = -0.7142857143

Simplifying
t = -0.7142857143
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {-0.7142857143, 1.5}