(3x+6)(x-1)=(x-1)(x+9)

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Solution for (3x+6)(x-1)=(x-1)(x+9) equation: 


Simplifying
(3x + 6)(x + -1) = (x + -1)(x + 9)

Reorder the terms:
(6 + 3x)(x + -1) = (x + -1)(x + 9)

Reorder the terms:
(6 + 3x)(-1 + x) = (x + -1)(x + 9)

Multiply (6 + 3x) * (-1 + x)
(6(-1 + x) + 3x * (-1 + x)) = (x + -1)(x + 9)
((-1 * 6 + x * 6) + 3x * (-1 + x)) = (x + -1)(x + 9)
((-6 + 6x) + 3x * (-1 + x)) = (x + -1)(x + 9)
(-6 + 6x + (-1 * 3x + x * 3x)) = (x + -1)(x + 9)
(-6 + 6x + (-3x + 3x2)) = (x + -1)(x + 9)

Combine like terms: 6x + -3x = 3x
(-6 + 3x + 3x2) = (x + -1)(x + 9)

Reorder the terms:
-6 + 3x + 3x2 = (-1 + x)(x + 9)

Reorder the terms:
-6 + 3x + 3x2 = (-1 + x)(9 + x)

Multiply (-1 + x) * (9 + x)
-6 + 3x + 3x2 = (-1(9 + x) + x(9 + x))
-6 + 3x + 3x2 = ((9 * -1 + x * -1) + x(9 + x))
-6 + 3x + 3x2 = ((-9 + -1x) + x(9 + x))
-6 + 3x + 3x2 = (-9 + -1x + (9 * x + x * x))
-6 + 3x + 3x2 = (-9 + -1x + (9x + x2))

Combine like terms: -1x + 9x = 8x
-6 + 3x + 3x2 = (-9 + 8x + x2)

Solving
-6 + 3x + 3x2 = -9 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 9 + 3x + -8x + 3x2 + -1x2 = -9 + 8x + x2 + 9 + -8x + -1x2

Combine like terms: -6 + 9 = 3
3 + 3x + -8x + 3x2 + -1x2 = -9 + 8x + x2 + 9 + -8x + -1x2

Combine like terms: 3x + -8x = -5x
3 + -5x + 3x2 + -1x2 = -9 + 8x + x2 + 9 + -8x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
3 + -5x + 2x2 = -9 + 8x + x2 + 9 + -8x + -1x2

Reorder the terms:
3 + -5x + 2x2 = -9 + 9 + 8x + -8x + x2 + -1x2

Combine like terms: -9 + 9 = 0
3 + -5x + 2x2 = 0 + 8x + -8x + x2 + -1x2
3 + -5x + 2x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
3 + -5x + 2x2 = 0 + x2 + -1x2
3 + -5x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -5x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1, 1.5}

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