(12a-15b)(10a+25b)=

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Solution for (12a-15b)(10a+25b)= equation: 


Simplifying
(12a + -15b)(10a + 25b) = 0

Multiply (12a + -15b) * (10a + 25b)
(12a * (10a + 25b) + -15b * (10a + 25b)) = 0
((10a * 12a + 25b * 12a) + -15b * (10a + 25b)) = 0

Reorder the terms:
((300ab + 120a2) + -15b * (10a + 25b)) = 0
((300ab + 120a2) + -15b * (10a + 25b)) = 0
(300ab + 120a2 + (10a * -15b + 25b * -15b)) = 0
(300ab + 120a2 + (-150ab + -375b2)) = 0

Reorder the terms:
(300ab + -150ab + 120a2 + -375b2) = 0

Combine like terms: 300ab + -150ab = 150ab
(150ab + 120a2 + -375b2) = 0

Solving
150ab + 120a2 + -375b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '15'.
15(10ab + 8a2 + -25b2) = 0

Factor a trinomial.
15((4a + -5b)(2a + 5b)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b

Subproblem 2
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
Solution
a = {1.25b, -2.5b}

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