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

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

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

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

Reorder the terms:
((4ab + 4a2) + -3b * (a + b)) = 0
((4ab + 4a2) + -3b * (a + b)) = 0
(4ab + 4a2 + (a * -3b + b * -3b)) = 0
(4ab + 4a2 + (-3ab + -3b2)) = 0

Reorder the terms:
(4ab + -3ab + 4a2 + -3b2) = 0

Combine like terms: 4ab + -3ab = 1ab
(1ab + 4a2 + -3b2) = 0

Solving
1ab + 4a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -3b)(a + b) = 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 '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {0.75b, -1b}