a(14+a)=2(5a+6)

Solution for a(14+a)=2(5a+6) equation:

Simplifying
a(14 + a) = 2(5a + 6)
(14 * a + a * a) = 2(5a + 6)
(14a + a2) = 2(5a + 6)

Reorder the terms:
14a + a2 = 2(6 + 5a)
14a + a2 = (6 * 2 + 5a * 2)
14a + a2 = (12 + 10a)

Solving
14a + a2 = 12 + 10a

Solving for variable 'a'.

Reorder the terms:
-12 + 14a + -10a + a2 = 12 + 10a + -12 + -10a

Combine like terms: 14a + -10a = 4a
-12 + 4a + a2 = 12 + 10a + -12 + -10a

Reorder the terms:
-12 + 4a + a2 = 12 + -12 + 10a + -10a

Combine like terms: 12 + -12 = 0
-12 + 4a + a2 = 0 + 10a + -10a
-12 + 4a + a2 = 10a + -10a

Combine like terms: 10a + -10a = 0
-12 + 4a + a2 = 0

Factor a trinomial.
(-6 + -1a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-6, 2}