(6x+17)(4x-13)=0

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Solution for (6x+17)(4x-13)=0 equation: 


Simplifying
(6x + 17)(4x + -13) = 0

Reorder the terms:
(17 + 6x)(4x + -13) = 0

Reorder the terms:
(17 + 6x)(-13 + 4x) = 0

Multiply (17 + 6x) * (-13 + 4x)
(17(-13 + 4x) + 6x * (-13 + 4x)) = 0
((-13 * 17 + 4x * 17) + 6x * (-13 + 4x)) = 0
((-221 + 68x) + 6x * (-13 + 4x)) = 0
(-221 + 68x + (-13 * 6x + 4x * 6x)) = 0
(-221 + 68x + (-78x + 24x2)) = 0

Combine like terms: 68x + -78x = -10x
(-221 + -10x + 24x2) = 0

Solving
-221 + -10x + 24x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -6x)(13 + -4x) = 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 '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {-2.833333333, 3.25}

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