17x(x-4)+138(x-4)=0

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Solution for 17x(x-4)+138(x-4)=0 equation: 


Simplifying
17x(x + -4) + 138(x + -4) = 0

Reorder the terms:
17x(-4 + x) + 138(x + -4) = 0
(-4 * 17x + x * 17x) + 138(x + -4) = 0
(-68x + 17x2) + 138(x + -4) = 0

Reorder the terms:
-68x + 17x2 + 138(-4 + x) = 0
-68x + 17x2 + (-4 * 138 + x * 138) = 0
-68x + 17x2 + (-552 + 138x) = 0

Reorder the terms:
-552 + -68x + 138x + 17x2 = 0

Combine like terms: -68x + 138x = 70x
-552 + 70x + 17x2 = 0

Solving
-552 + 70x + 17x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-138 + -17x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-138 + -17x)' equal to zero and attempt to solve:

Simplifying
-138 + -17x = 0

Solving
-138 + -17x = 0

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

Add '138' to each side of the equation.
-138 + 138 + -17x = 0 + 138

Combine like terms: -138 + 138 = 0
0 + -17x = 0 + 138
-17x = 0 + 138

Combine like terms: 0 + 138 = 138
-17x = 138

Divide each side by '-17'.
x = -8.117647059

Simplifying
x = -8.117647059

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8.117647059, 4}

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