(2a-5b)x(3a+b)=

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Solution for (2a-5b)x(3a+b)= equation: 


Simplifying
(2a + -5b) * x(3a + b) = 0

Reorder the terms for easier multiplication:
x(2a + -5b)(3a + b) = 0

Multiply (2a + -5b) * (3a + b)
x(2a * (3a + b) + -5b * (3a + b)) = 0
x((3a * 2a + b * 2a) + -5b * (3a + b)) = 0

Reorder the terms:
x((2ab + 6a2) + -5b * (3a + b)) = 0
x((2ab + 6a2) + -5b * (3a + b)) = 0
x(2ab + 6a2 + (3a * -5b + b * -5b)) = 0
x(2ab + 6a2 + (-15ab + -5b2)) = 0

Reorder the terms:
x(2ab + -15ab + 6a2 + -5b2) = 0

Combine like terms: 2ab + -15ab = -13ab
x(-13ab + 6a2 + -5b2) = 0
(-13ab * x + 6a2 * x + -5b2 * x) = 0
(-13abx + 6a2x + -5b2x) = 0

Solving
-13abx + 6a2x + -5b2x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13ab + 6a2 + -5b2) = 0

Factor a trinomial.
x((2a + -5b)(3a + b)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Subproblem 3
Set the factor '(3a + b)' equal to zero and attempt to solve:

Simplifying
3a + b = 0

Solving
3a + b = 0

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

Add '-1b' to each side of the equation.
3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
3a + 0 = 0 + -1b
3a = 0 + -1b
Remove the zero:
3a = -1b

Divide each side by '3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b
Solution
a = {2.5b, -0.3333333333b}

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