(2a+41)x(5a-4)=

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Solution for (2a+41)x(5a-4)= equation: 


Simplifying
(2a + 41) * x(5a + -4) = 0

Reorder the terms:
(41 + 2a) * x(5a + -4) = 0

Reorder the terms:
(41 + 2a) * x(-4 + 5a) = 0

Reorder the terms for easier multiplication:
x(41 + 2a)(-4 + 5a) = 0

Multiply (41 + 2a) * (-4 + 5a)
x(41(-4 + 5a) + 2a * (-4 + 5a)) = 0
x((-4 * 41 + 5a * 41) + 2a * (-4 + 5a)) = 0
x((-164 + 205a) + 2a * (-4 + 5a)) = 0
x(-164 + 205a + (-4 * 2a + 5a * 2a)) = 0
x(-164 + 205a + (-8a + 10a2)) = 0

Combine like terms: 205a + -8a = 197a
x(-164 + 197a + 10a2) = 0
(-164 * x + 197a * x + 10a2 * x) = 0

Reorder the terms:
(197ax + 10a2x + -164x) = 0
(197ax + 10a2x + -164x) = 0

Solving
197ax + 10a2x + -164x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(197a + 10a2 + -164) = 0

Factor a trinomial.
x((5a + -4)(2a + 41)) = 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 '(5a + -4)' equal to zero and attempt to solve:

Simplifying
5a + -4 = 0

Reorder the terms:
-4 + 5a = 0

Solving
-4 + 5a = 0

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

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

Combine like terms: -4 + 4 = 0
0 + 5a = 0 + 4
5a = 0 + 4

Combine like terms: 0 + 4 = 4
5a = 4

Divide each side by '5'.
a = 0.8

Simplifying
a = 0.8

Subproblem 3
Set the factor '(2a + 41)' equal to zero and attempt to solve:

Simplifying
2a + 41 = 0

Reorder the terms:
41 + 2a = 0

Solving
41 + 2a = 0

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

Add '-41' to each side of the equation.
41 + -41 + 2a = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 2a = 0 + -41
2a = 0 + -41

Combine like terms: 0 + -41 = -41
2a = -41

Divide each side by '2'.
a = -20.5

Simplifying
a = -20.5
Solution
a = {0.8, -20.5}

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