(3x-1)(x-9)=4x(x-9)

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Solution for (3x-1)(x-9)=4x(x-9) equation: 


Simplifying
(3x + -1)(x + -9) = 4x(x + -9)

Reorder the terms:
(-1 + 3x)(x + -9) = 4x(x + -9)

Reorder the terms:
(-1 + 3x)(-9 + x) = 4x(x + -9)

Multiply (-1 + 3x) * (-9 + x)
(-1(-9 + x) + 3x * (-9 + x)) = 4x(x + -9)
((-9 * -1 + x * -1) + 3x * (-9 + x)) = 4x(x + -9)
((9 + -1x) + 3x * (-9 + x)) = 4x(x + -9)
(9 + -1x + (-9 * 3x + x * 3x)) = 4x(x + -9)
(9 + -1x + (-27x + 3x2)) = 4x(x + -9)

Combine like terms: -1x + -27x = -28x
(9 + -28x + 3x2) = 4x(x + -9)

Reorder the terms:
9 + -28x + 3x2 = 4x(-9 + x)
9 + -28x + 3x2 = (-9 * 4x + x * 4x)
9 + -28x + 3x2 = (-36x + 4x2)

Solving
9 + -28x + 3x2 = -36x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -28x + 36x + 3x2 + -4x2 = -36x + 4x2 + 36x + -4x2

Combine like terms: -28x + 36x = 8x
9 + 8x + 3x2 + -4x2 = -36x + 4x2 + 36x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
9 + 8x + -1x2 = -36x + 4x2 + 36x + -4x2

Reorder the terms:
9 + 8x + -1x2 = -36x + 36x + 4x2 + -4x2

Combine like terms: -36x + 36x = 0
9 + 8x + -1x2 = 0 + 4x2 + -4x2
9 + 8x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + 8x + -1x2 = 0

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


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

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {9, -1}

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