(4a+3b)(-7a+3b)=

Solution for (4a+3b)(-7a+3b)= equation:

Simplifying
(4a + 3b)(-7a + 3b) = 0

Multiply (4a + 3b) * (-7a + 3b)
(4a * (-7a + 3b) + 3b * (-7a + 3b)) = 0
((-7a * 4a + 3b * 4a) + 3b * (-7a + 3b)) = 0

Reorder the terms:
((12ab + -28a2) + 3b * (-7a + 3b)) = 0
((12ab + -28a2) + 3b * (-7a + 3b)) = 0
(12ab + -28a2 + (-7a * 3b + 3b * 3b)) = 0
(12ab + -28a2 + (-21ab + 9b2)) = 0

Reorder the terms:
(12ab + -21ab + -28a2 + 9b2) = 0

Combine like terms: 12ab + -21ab = -9ab
(-9ab + -28a2 + 9b2) = 0

Solving
-9ab + -28a2 + 9b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4a + -3b)(7a + -3b) = 0

Subproblem 1
Set the factor '(-4a + -3b)' equal to zero and attempt to solve:

Simplifying
-4a + -3b = 0

Solving
-4a + -3b = 0

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

Add '3b' to each side of the equation.
-4a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
-4a + 0 = 0 + 3b
-4a = 0 + 3b
Remove the zero:
-4a = 3b

Divide each side by '-4'.
a = -0.75b

Simplifying
a = -0.75b
Subproblem 2
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
Solution
a = {-0.75b, 0.4285714286b}