9x(x-3)=(2x+8)(x-3)

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Solution for 9x(x-3)=(2x+8)(x-3) equation: 


Simplifying
9x(x + -3) = (2x + 8)(x + -3)

Reorder the terms:
9x(-3 + x) = (2x + 8)(x + -3)
(-3 * 9x + x * 9x) = (2x + 8)(x + -3)
(-27x + 9x2) = (2x + 8)(x + -3)

Reorder the terms:
-27x + 9x2 = (8 + 2x)(x + -3)

Reorder the terms:
-27x + 9x2 = (8 + 2x)(-3 + x)

Multiply (8 + 2x) * (-3 + x)
-27x + 9x2 = (8(-3 + x) + 2x * (-3 + x))
-27x + 9x2 = ((-3 * 8 + x * 8) + 2x * (-3 + x))
-27x + 9x2 = ((-24 + 8x) + 2x * (-3 + x))
-27x + 9x2 = (-24 + 8x + (-3 * 2x + x * 2x))
-27x + 9x2 = (-24 + 8x + (-6x + 2x2))

Combine like terms: 8x + -6x = 2x
-27x + 9x2 = (-24 + 2x + 2x2)

Solving
-27x + 9x2 = -24 + 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
24 + -27x + -2x + 9x2 + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Combine like terms: -27x + -2x = -29x
24 + -29x + 9x2 + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Combine like terms: 9x2 + -2x2 = 7x2
24 + -29x + 7x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Reorder the terms:
24 + -29x + 7x2 = -24 + 24 + 2x + -2x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
24 + -29x + 7x2 = 0 + 2x + -2x + 2x2 + -2x2
24 + -29x + 7x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
24 + -29x + 7x2 = 0 + 2x2 + -2x2
24 + -29x + 7x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + -29x + 7x2 = 0

Factor a trinomial.
(8 + -7x)(3 + -1x) = 0


Subproblem 1
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.142857143, 3}

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