x(9x+4)=1(9x+4)

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Solution for x(9x+4)=1(9x+4) equation: 


Simplifying
x(9x + 4) = 1(9x + 4)

Reorder the terms:
x(4 + 9x) = 1(9x + 4)
(4 * x + 9x * x) = 1(9x + 4)
(4x + 9x2) = 1(9x + 4)

Reorder the terms:
4x + 9x2 = 1(4 + 9x)
4x + 9x2 = (4 * 1 + 9x * 1)
4x + 9x2 = (4 + 9x)

Solving
4x + 9x2 = 4 + 9x

Solving for variable 'x'.

Reorder the terms:
-4 + 4x + -9x + 9x2 = 4 + 9x + -4 + -9x

Combine like terms: 4x + -9x = -5x
-4 + -5x + 9x2 = 4 + 9x + -4 + -9x

Reorder the terms:
-4 + -5x + 9x2 = 4 + -4 + 9x + -9x

Combine like terms: 4 + -4 = 0
-4 + -5x + 9x2 = 0 + 9x + -9x
-4 + -5x + 9x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-4 + -5x + 9x2 = 0

Factor a trinomial.
(-4 + -9x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x = 0 + 4
-9x = 0 + 4

Combine like terms: 0 + 4 = 4
-9x = 4

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.4444444444, 1}

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