(4a-3)(2a+3a+5)=

Solution for (4a-3)(2a+3a+5)= equation:

Simplifying
(4a + -3)(2a + 3a + 5) = 0

Reorder the terms:
(-3 + 4a)(2a + 3a + 5) = 0

Reorder the terms:
(-3 + 4a)(5 + 2a + 3a) = 0

Combine like terms: 2a + 3a = 5a
(-3 + 4a)(5 + 5a) = 0

Multiply (-3 + 4a) * (5 + 5a)
(-3(5 + 5a) + 4a * (5 + 5a)) = 0
((5 * -3 + 5a * -3) + 4a * (5 + 5a)) = 0
((-15 + -15a) + 4a * (5 + 5a)) = 0
(-15 + -15a + (5 * 4a + 5a * 4a)) = 0
(-15 + -15a + (20a + 20a2)) = 0

Combine like terms: -15a + 20a = 5a
(-15 + 5a + 20a2) = 0

Solving
-15 + 5a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + a + 4a2) = 0

Factor a trinomial.
5((-1 + -1a)(3 + -4a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -1a)' equal to zero and attempt to solve:

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1a = 0 + 1
-1a = 0 + 1

Combine like terms: 0 + 1 = 1
-1a = 1

Divide each side by '-1'.
a = -1

Simplifying
a = -1
Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-1, 0.75}