2a(2a-3)=10

Solution for 2a(2a-3)=10 equation:

Simplifying
2a(2a + -3) = 10

Reorder the terms:
2a(-3 + 2a) = 10
(-3 * 2a + 2a * 2a) = 10
(-6a + 4a2) = 10

Solving
-6a + 4a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + -6a + 4a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -6a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3a + 2a2) = 0

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

Ignore the factor 2.
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 '(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
Solution
a = {-1, 2.5}