(3+ab)(7-ab)=

Solution for (3+ab)(7-ab)= equation:

Simplifying
(3 + ab)(7 + -1ab) = 0

Multiply (3 + ab) * (7 + -1ab)
(3(7 + -1ab) + ab(7 + -1ab)) = 0
((7 * 3 + -1ab * 3) + ab(7 + -1ab)) = 0
((21 + -3ab) + ab(7 + -1ab)) = 0
(21 + -3ab + (7 * ab + -1ab * ab)) = 0
(21 + -3ab + (7ab + -1a2b2)) = 0

Combine like terms: -3ab + 7ab = 4ab
(21 + 4ab + -1a2b2) = 0

Solving
21 + 4ab + -1a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + -1ab)(3 + ab) = 0

Subproblem 1
Set the factor '(7 + -1ab)' equal to zero and attempt to solve:

Simplifying
7 + -1ab = 0

Solving
7 + -1ab = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1ab = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1ab = 0 + -7
-1ab = 0 + -7

Combine like terms: 0 + -7 = -7
-1ab = -7

Divide each side by '-1b'.
a = 7b-1

Simplifying
a = 7b-1
Subproblem 2
Set the factor '(3 + ab)' equal to zero and attempt to solve:

Simplifying
3 + ab = 0

Solving
3 + ab = 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 + ab = 0 + -3

Combine like terms: 3 + -3 = 0
0 + ab = 0 + -3
ab = 0 + -3

Combine like terms: 0 + -3 = -3
ab = -3

Divide each side by 'b'.
a = -3b-1

Simplifying
a = -3b-1
Solution
a = {7b-1, -3b-1}