12a+14ab=2a(6a+7b)

Solution for 12a+14ab=2a(6a+7b) equation:

Simplifying
12a + 14ab = 2a(6a + 7b)
12a + 14ab = (6a * 2a + 7b * 2a)

Reorder the terms:
12a + 14ab = (14ab + 12a2)
12a + 14ab = (14ab + 12a2)

Add '-14ab' to each side of the equation.
12a + 14ab + -14ab = 14ab + -14ab + 12a2

Combine like terms: 14ab + -14ab = 0
12a + 0 = 14ab + -14ab + 12a2
12a = 14ab + -14ab + 12a2

Combine like terms: 14ab + -14ab = 0
12a = 0 + 12a2
12a = 12a2

Solving
12a = 12a2

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '12a'.
12a(1 + -1a) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
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
Solution
a = {0, 1}