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

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


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

Reorder the terms:
8x(-3 + x) = (2x + 9)(x + -3)
(-3 * 8x + x * 8x) = (2x + 9)(x + -3)
(-24x + 8x2) = (2x + 9)(x + -3)

Reorder the terms:
-24x + 8x2 = (9 + 2x)(x + -3)

Reorder the terms:
-24x + 8x2 = (9 + 2x)(-3 + x)

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

Combine like terms: 9x + -6x = 3x
-24x + 8x2 = (-27 + 3x + 2x2)

Solving
-24x + 8x2 = -27 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
27 + -24x + -3x + 8x2 + -2x2 = -27 + 3x + 2x2 + 27 + -3x + -2x2

Combine like terms: -24x + -3x = -27x
27 + -27x + 8x2 + -2x2 = -27 + 3x + 2x2 + 27 + -3x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
27 + -27x + 6x2 = -27 + 3x + 2x2 + 27 + -3x + -2x2

Reorder the terms:
27 + -27x + 6x2 = -27 + 27 + 3x + -3x + 2x2 + -2x2

Combine like terms: -27 + 27 = 0
27 + -27x + 6x2 = 0 + 3x + -3x + 2x2 + -2x2
27 + -27x + 6x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
27 + -27x + 6x2 = 0 + 2x2 + -2x2
27 + -27x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
27 + -27x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -9x + 2x2) = 0

Factor a trinomial.
3((3 + -2x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
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

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 = {1.5, 3}

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