(6x+17)(9x-4)=0

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Solution for (6x+17)(9x-4)=0 equation: 


Simplifying
(6x + 17)(9x + -4) = 0

Reorder the terms:
(17 + 6x)(9x + -4) = 0

Reorder the terms:
(17 + 6x)(-4 + 9x) = 0

Multiply (17 + 6x) * (-4 + 9x)
(17(-4 + 9x) + 6x * (-4 + 9x)) = 0
((-4 * 17 + 9x * 17) + 6x * (-4 + 9x)) = 0
((-68 + 153x) + 6x * (-4 + 9x)) = 0
(-68 + 153x + (-4 * 6x + 9x * 6x)) = 0
(-68 + 153x + (-24x + 54x2)) = 0

Combine like terms: 153x + -24x = 129x
(-68 + 129x + 54x2) = 0

Solving
-68 + 129x + 54x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -6x)(4 + -9x) = 0


Subproblem 1
Set the factor '(-17 + -6x)' equal to zero and attempt to solve:

Simplifying
-17 + -6x = 0

Solving
-17 + -6x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -6x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -6x = 0 + 17
-6x = 0 + 17

Combine like terms: 0 + 17 = 17
-6x = 17

Divide each side by '-6'.
x = -2.833333333

Simplifying
x = -2.833333333

Subproblem 2
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444
Solution
x = {-2.833333333, 0.4444444444}

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