8x(2x-1)-(2x-1)(3x+9)=0

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Solution for 8x(2x-1)-(2x-1)(3x+9)=0 equation: 


Simplifying
8x(2x + -1) + -1(2x + -1)(3x + 9) = 0

Reorder the terms:
8x(-1 + 2x) + -1(2x + -1)(3x + 9) = 0
(-1 * 8x + 2x * 8x) + -1(2x + -1)(3x + 9) = 0
(-8x + 16x2) + -1(2x + -1)(3x + 9) = 0

Reorder the terms:
-8x + 16x2 + -1(-1 + 2x)(3x + 9) = 0

Reorder the terms:
-8x + 16x2 + -1(-1 + 2x)(9 + 3x) = 0

Multiply (-1 + 2x) * (9 + 3x)
-8x + 16x2 + -1(-1(9 + 3x) + 2x * (9 + 3x)) = 0
-8x + 16x2 + -1((9 * -1 + 3x * -1) + 2x * (9 + 3x)) = 0
-8x + 16x2 + -1((-9 + -3x) + 2x * (9 + 3x)) = 0
-8x + 16x2 + -1(-9 + -3x + (9 * 2x + 3x * 2x)) = 0
-8x + 16x2 + -1(-9 + -3x + (18x + 6x2)) = 0

Combine like terms: -3x + 18x = 15x
-8x + 16x2 + -1(-9 + 15x + 6x2) = 0
-8x + 16x2 + (-9 * -1 + 15x * -1 + 6x2 * -1) = 0
-8x + 16x2 + (9 + -15x + -6x2) = 0

Reorder the terms:
9 + -8x + -15x + 16x2 + -6x2 = 0

Combine like terms: -8x + -15x = -23x
9 + -23x + 16x2 + -6x2 = 0

Combine like terms: 16x2 + -6x2 = 10x2
9 + -23x + 10x2 = 0

Solving
9 + -23x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(9 + -5x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {0.5, 1.8}

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