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

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

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

Multiply (4a + -3t) * (4a + 2t)
(4a * (4a + 2t) + -3t * (4a + 2t)) = 0
((4a * 4a + 2t * 4a) + -3t * (4a + 2t)) = 0

Reorder the terms:
((8at + 16a2) + -3t * (4a + 2t)) = 0
((8at + 16a2) + -3t * (4a + 2t)) = 0
(8at + 16a2 + (4a * -3t + 2t * -3t)) = 0
(8at + 16a2 + (-12at + -6t2)) = 0

Reorder the terms:
(8at + -12at + 16a2 + -6t2) = 0

Combine like terms: 8at + -12at = -4at
(-4at + 16a2 + -6t2) = 0

Solving
-4at + 16a2 + -6t2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2at + 8a2 + -3t2) = 0

Factor a trinomial.
2((4a + -3t)(2a + t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4a + -3t)' equal to zero and attempt to solve:

Simplifying
4a + -3t = 0

Solving
4a + -3t = 0

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

Add '3t' to each side of the equation.
4a + -3t + 3t = 0 + 3t

Combine like terms: -3t + 3t = 0
4a + 0 = 0 + 3t
4a = 0 + 3t
Remove the zero:
4a = 3t

Divide each side by '4'.
a = 0.75t

Simplifying
a = 0.75t
Subproblem 2
Set the factor '(2a + t)' equal to zero and attempt to solve:

Simplifying
2a + t = 0

Solving
2a + t = 0

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

Add '-1t' to each side of the equation.
2a + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
2a + 0 = 0 + -1t
2a = 0 + -1t
Remove the zero:
2a = -1t

Divide each side by '2'.
a = -0.5t

Simplifying
a = -0.5t
Solution
a = {0.75t, -0.5t}