a^2=2(10a-48)

Solution for a^2=2(10a-48) equation:

Simplifying
a2 = 2(10a + -48)

Reorder the terms:
a2 = 2(-48 + 10a)
a2 = (-48 * 2 + 10a * 2)
a2 = (-96 + 20a)

Solving
a2 = -96 + 20a

Solving for variable 'a'.

Reorder the terms:
96 + -20a + a2 = -96 + 20a + 96 + -20a

Reorder the terms:
96 + -20a + a2 = -96 + 96 + 20a + -20a

Combine like terms: -96 + 96 = 0
96 + -20a + a2 = 0 + 20a + -20a
96 + -20a + a2 = 20a + -20a

Combine like terms: 20a + -20a = 0
96 + -20a + a2 = 0

Factor a trinomial.
(8 + -1a)(12 + -1a) = 0

Subproblem 1
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {8, 12}