(4a+6b)(a-10b)=

Solution for (4a+6b)(a-10b)= equation:

Simplifying
(4a + 6b)(a + -10b) = 0

Multiply (4a + 6b) * (a + -10b)
(4a * (a + -10b) + 6b * (a + -10b)) = 0
((a * 4a + -10b * 4a) + 6b * (a + -10b)) = 0

Reorder the terms:
((-40ab + 4a2) + 6b * (a + -10b)) = 0
((-40ab + 4a2) + 6b * (a + -10b)) = 0
(-40ab + 4a2 + (a * 6b + -10b * 6b)) = 0
(-40ab + 4a2 + (6ab + -60b2)) = 0

Reorder the terms:
(-40ab + 6ab + 4a2 + -60b2) = 0

Combine like terms: -40ab + 6ab = -34ab
(-34ab + 4a2 + -60b2) = 0

Solving
-34ab + 4a2 + -60b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17ab + 2a2 + -30b2) = 0

Factor a trinomial.
2((a + -10b)(2a + 3b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(a + -10b)' equal to zero and attempt to solve:

Simplifying
a + -10b = 0

Solving
a + -10b = 0

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

Add '10b' to each side of the equation.
a + -10b + 10b = 0 + 10b

Combine like terms: -10b + 10b = 0
a + 0 = 0 + 10b
a = 0 + 10b
Remove the zero:
a = 10b

Simplifying
a = 10b
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 = {10b, -1.5b}