(x-1)(3x-1)=(x+8)(x-1)

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Solution for (x-1)(3x-1)=(x+8)(x-1) equation: 


Simplifying
(x + -1)(3x + -1) = (x + 8)(x + -1)

Reorder the terms:
(-1 + x)(3x + -1) = (x + 8)(x + -1)

Reorder the terms:
(-1 + x)(-1 + 3x) = (x + 8)(x + -1)

Multiply (-1 + x) * (-1 + 3x)
(-1(-1 + 3x) + x(-1 + 3x)) = (x + 8)(x + -1)
((-1 * -1 + 3x * -1) + x(-1 + 3x)) = (x + 8)(x + -1)
((1 + -3x) + x(-1 + 3x)) = (x + 8)(x + -1)
(1 + -3x + (-1 * x + 3x * x)) = (x + 8)(x + -1)
(1 + -3x + (-1x + 3x2)) = (x + 8)(x + -1)

Combine like terms: -3x + -1x = -4x
(1 + -4x + 3x2) = (x + 8)(x + -1)

Reorder the terms:
1 + -4x + 3x2 = (8 + x)(x + -1)

Reorder the terms:
1 + -4x + 3x2 = (8 + x)(-1 + x)

Multiply (8 + x) * (-1 + x)
1 + -4x + 3x2 = (8(-1 + x) + x(-1 + x))
1 + -4x + 3x2 = ((-1 * 8 + x * 8) + x(-1 + x))
1 + -4x + 3x2 = ((-8 + 8x) + x(-1 + x))
1 + -4x + 3x2 = (-8 + 8x + (-1 * x + x * x))
1 + -4x + 3x2 = (-8 + 8x + (-1x + x2))

Combine like terms: 8x + -1x = 7x
1 + -4x + 3x2 = (-8 + 7x + x2)

Solving
1 + -4x + 3x2 = -8 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
1 + 8 + -4x + -7x + 3x2 + -1x2 = -8 + 7x + x2 + 8 + -7x + -1x2

Combine like terms: 1 + 8 = 9
9 + -4x + -7x + 3x2 + -1x2 = -8 + 7x + x2 + 8 + -7x + -1x2

Combine like terms: -4x + -7x = -11x
9 + -11x + 3x2 + -1x2 = -8 + 7x + x2 + 8 + -7x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
9 + -11x + 2x2 = -8 + 7x + x2 + 8 + -7x + -1x2

Reorder the terms:
9 + -11x + 2x2 = -8 + 8 + 7x + -7x + x2 + -1x2

Combine like terms: -8 + 8 = 0
9 + -11x + 2x2 = 0 + 7x + -7x + x2 + -1x2
9 + -11x + 2x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
9 + -11x + 2x2 = 0 + x2 + -1x2
9 + -11x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + -11x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -2x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1, 4.5}

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