9x(x-5)=(2x+1)(9x-5)

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Solution for 9x(x-5)=(2x+1)(9x-5) equation: 


Simplifying
9x(x + -5) = (2x + 1)(9x + -5)

Reorder the terms:
9x(-5 + x) = (2x + 1)(9x + -5)
(-5 * 9x + x * 9x) = (2x + 1)(9x + -5)
(-45x + 9x2) = (2x + 1)(9x + -5)

Reorder the terms:
-45x + 9x2 = (1 + 2x)(9x + -5)

Reorder the terms:
-45x + 9x2 = (1 + 2x)(-5 + 9x)

Multiply (1 + 2x) * (-5 + 9x)
-45x + 9x2 = (1(-5 + 9x) + 2x * (-5 + 9x))
-45x + 9x2 = ((-5 * 1 + 9x * 1) + 2x * (-5 + 9x))
-45x + 9x2 = ((-5 + 9x) + 2x * (-5 + 9x))
-45x + 9x2 = (-5 + 9x + (-5 * 2x + 9x * 2x))
-45x + 9x2 = (-5 + 9x + (-10x + 18x2))

Combine like terms: 9x + -10x = -1x
-45x + 9x2 = (-5 + -1x + 18x2)

Solving
-45x + 9x2 = -5 + -1x + 18x2

Solving for variable 'x'.

Reorder the terms:
5 + -45x + x + 9x2 + -18x2 = -5 + -1x + 18x2 + 5 + x + -18x2

Combine like terms: -45x + x = -44x
5 + -44x + 9x2 + -18x2 = -5 + -1x + 18x2 + 5 + x + -18x2

Combine like terms: 9x2 + -18x2 = -9x2
5 + -44x + -9x2 = -5 + -1x + 18x2 + 5 + x + -18x2

Reorder the terms:
5 + -44x + -9x2 = -5 + 5 + -1x + x + 18x2 + -18x2

Combine like terms: -5 + 5 = 0
5 + -44x + -9x2 = 0 + -1x + x + 18x2 + -18x2
5 + -44x + -9x2 = -1x + x + 18x2 + -18x2

Combine like terms: -1x + x = 0
5 + -44x + -9x2 = 0 + 18x2 + -18x2
5 + -44x + -9x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
5 + -44x + -9x2 = 0

Factor a trinomial.
(1 + -9x)(5 + x) = 0


Subproblem 1
Set the factor '(1 + -9x)' equal to zero and attempt to solve:

Simplifying
1 + -9x = 0

Solving
1 + -9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9x = 0 + -1
-9x = 0 + -1

Combine like terms: 0 + -1 = -1
-9x = -1

Divide each side by '-9'.
x = 0.1111111111

Simplifying
x = 0.1111111111

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0.1111111111, -5}

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