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

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


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

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

Reorder the terms:
((4ab + 24a2) + -10b * (6a + b)) = 0
((4ab + 24a2) + -10b * (6a + b)) = 0
(4ab + 24a2 + (6a * -10b + b * -10b)) = 0
(4ab + 24a2 + (-60ab + -10b2)) = 0

Reorder the terms:
(4ab + -60ab + 24a2 + -10b2) = 0

Combine like terms: 4ab + -60ab = -56ab
(-56ab + 24a2 + -10b2) = 0

Solving
-56ab + 24a2 + -10b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28ab + 12a2 + -5b2) = 0

Factor a trinomial.
2((2a + -5b)(6a + b)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2a + -5b)' equal to zero and attempt to solve:

Simplifying
2a + -5b = 0

Solving
2a + -5b = 0

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

Add '5b' to each side of the equation.
2a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
2a + 0 = 0 + 5b
2a = 0 + 5b
Remove the zero:
2a = 5b

Divide each side by '2'.
a = 2.5b

Simplifying
a = 2.5b

Subproblem 2
Set the factor '(6a + b)' equal to zero and attempt to solve:

Simplifying
6a + b = 0

Solving
6a + b = 0

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

Add '-1b' to each side of the equation.
6a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
6a + 0 = 0 + -1b
6a = 0 + -1b
Remove the zero:
6a = -1b

Divide each side by '6'.
a = -0.1666666667b

Simplifying
a = -0.1666666667b
Solution
a = {2.5b, -0.1666666667b}

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