(2a-3b)(a-7b)=

Solution for (2a-3b)(a-7b)= equation:

Simplifying
(2a + -3b)(a + -7b) = 0

Multiply (2a + -3b) * (a + -7b)
(2a * (a + -7b) + -3b * (a + -7b)) = 0
((a * 2a + -7b * 2a) + -3b * (a + -7b)) = 0

Reorder the terms:
((-14ab + 2a2) + -3b * (a + -7b)) = 0
((-14ab + 2a2) + -3b * (a + -7b)) = 0
(-14ab + 2a2 + (a * -3b + -7b * -3b)) = 0
(-14ab + 2a2 + (-3ab + 21b2)) = 0

Reorder the terms:
(-14ab + -3ab + 2a2 + 21b2) = 0

Combine like terms: -14ab + -3ab = -17ab
(-17ab + 2a2 + 21b2) = 0

Solving
-17ab + 2a2 + 21b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -7b)(2a + -3b) = 0

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

Simplifying
a + -7b = 0

Solving
a + -7b = 0

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

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

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

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

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b
Solution
a = {7b, 1.5b}