(7a-3b)*(a+12b)=

Solution for (7a-3b)*(a+12b)= equation:

Simplifying
(7a + -3b)(a + 12b) = 0

Multiply (7a + -3b) * (a + 12b)
(7a * (a + 12b) + -3b * (a + 12b)) = 0
((a * 7a + 12b * 7a) + -3b * (a + 12b)) = 0

Reorder the terms:
((84ab + 7a2) + -3b * (a + 12b)) = 0
((84ab + 7a2) + -3b * (a + 12b)) = 0
(84ab + 7a2 + (a * -3b + 12b * -3b)) = 0
(84ab + 7a2 + (-3ab + -36b2)) = 0

Reorder the terms:
(84ab + -3ab + 7a2 + -36b2) = 0

Combine like terms: 84ab + -3ab = 81ab
(81ab + 7a2 + -36b2) = 0

Solving
81ab + 7a2 + -36b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7a + -3b)(a + 12b) = 0

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

Simplifying
7a + -3b = 0

Solving
7a + -3b = 0

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

Add '3b' to each side of the equation.
7a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
7a + 0 = 0 + 3b
7a = 0 + 3b
Remove the zero:
7a = 3b

Divide each side by '7'.
a = 0.4285714286b

Simplifying
a = 0.4285714286b
Subproblem 2
Set the factor '(a + 12b)' equal to zero and attempt to solve:

Simplifying
a + 12b = 0

Solving
a + 12b = 0

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

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

Combine like terms: 12b + -12b = 0
a + 0 = 0 + -12b
a = 0 + -12b
Remove the zero:
a = -12b

Simplifying
a = -12b
Solution
a = {0.4285714286b, -12b}