(13x+9)(6x-3)x=

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Solution for (13x+9)(6x-3)x= equation: 


Simplifying
(13x + 9)(6x + -3) * x = 0

Reorder the terms:
(9 + 13x)(6x + -3) * x = 0

Reorder the terms:
(9 + 13x)(-3 + 6x) * x = 0

Reorder the terms for easier multiplication:
x(9 + 13x)(-3 + 6x) = 0

Multiply (9 + 13x) * (-3 + 6x)
x(9(-3 + 6x) + 13x * (-3 + 6x)) = 0
x((-3 * 9 + 6x * 9) + 13x * (-3 + 6x)) = 0
x((-27 + 54x) + 13x * (-3 + 6x)) = 0
x(-27 + 54x + (-3 * 13x + 6x * 13x)) = 0
x(-27 + 54x + (-39x + 78x2)) = 0

Combine like terms: 54x + -39x = 15x
x(-27 + 15x + 78x2) = 0
(-27 * x + 15x * x + 78x2 * x) = 0
(-27x + 15x2 + 78x3) = 0

Solving
-27x + 15x2 + 78x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + 5x + 26x2) = 0

Factor a trinomial.
3x((-9 + -13x)(1 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-9 + -13x)' equal to zero and attempt to solve:

Simplifying
-9 + -13x = 0

Solving
-9 + -13x = 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 + -13x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -13x = 0 + 9
-13x = 0 + 9

Combine like terms: 0 + 9 = 9
-13x = 9

Divide each side by '-13'.
x = -0.6923076923

Simplifying
x = -0.6923076923

Subproblem 3
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
Solution
x = {0, -0.6923076923, 0.5}

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