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

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

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

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

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

Multiply (-5 + 2a) * (-3 + a)
2(-5(-3 + a) + 2a * (-3 + a)) = 0
2((-3 * -5 + a * -5) + 2a * (-3 + a)) = 0
2((15 + -5a) + 2a * (-3 + a)) = 0
2(15 + -5a + (-3 * 2a + a * 2a)) = 0
2(15 + -5a + (-6a + 2a2)) = 0

Combine like terms: -5a + -6a = -11a
2(15 + -11a + 2a2) = 0
(15 * 2 + -11a * 2 + 2a2 * 2) = 0
(30 + -22a + 4a2) = 0

Solving
30 + -22a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -11a + 2a2) = 0

Factor a trinomial.
2((5 + -2a)(3 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {2.5, 3}