(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 = -11ab
(-11ab + 2a2 + -21b2) = 0

Solving
-11ab + 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}