a(10+a)=3(3a+4)

Solution for a(10+a)=3(3a+4) equation:

Simplifying
a(10 + a) = 3(3a + 4)
(10 * a + a * a) = 3(3a + 4)
(10a + a2) = 3(3a + 4)

Reorder the terms:
10a + a2 = 3(4 + 3a)
10a + a2 = (4 * 3 + 3a * 3)
10a + a2 = (12 + 9a)

Solving
10a + a2 = 12 + 9a

Solving for variable 'a'.

Reorder the terms:
-12 + 10a + -9a + a2 = 12 + 9a + -12 + -9a

Combine like terms: 10a + -9a = 1a
-12 + 1a + a2 = 12 + 9a + -12 + -9a

Reorder the terms:
-12 + 1a + a2 = 12 + -12 + 9a + -9a

Combine like terms: 12 + -12 = 0
-12 + 1a + a2 = 0 + 9a + -9a
-12 + 1a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-12 + 1a + a2 = 0

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

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

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
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 = {-4, 3}