18x^2-30x-100=67x+30

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Solution for 18x^2-30x-100=67x+30 equation: 


Simplifying
18x2 + -30x + -100 = 67x + 30

Reorder the terms:
-100 + -30x + 18x2 = 67x + 30

Reorder the terms:
-100 + -30x + 18x2 = 30 + 67x

Solving
-100 + -30x + 18x2 = 30 + 67x

Solving for variable 'x'.

Reorder the terms:
-100 + -30 + -30x + -67x + 18x2 = 30 + 67x + -30 + -67x

Combine like terms: -100 + -30 = -130
-130 + -30x + -67x + 18x2 = 30 + 67x + -30 + -67x

Combine like terms: -30x + -67x = -97x
-130 + -97x + 18x2 = 30 + 67x + -30 + -67x

Reorder the terms:
-130 + -97x + 18x2 = 30 + -30 + 67x + -67x

Combine like terms: 30 + -30 = 0
-130 + -97x + 18x2 = 0 + 67x + -67x
-130 + -97x + 18x2 = 67x + -67x

Combine like terms: 67x + -67x = 0
-130 + -97x + 18x2 = 0

Factor a trinomial.
(-10 + -9x)(13 + -2x) = 0


Subproblem 1
Set the factor '(-10 + -9x)' equal to zero and attempt to solve:

Simplifying
-10 + -9x = 0

Solving
-10 + -9x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -9x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -9x = 0 + 10
-9x = 0 + 10

Combine like terms: 0 + 10 = 10
-9x = 10

Divide each side by '-9'.
x = -1.111111111

Simplifying
x = -1.111111111

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

Simplifying
13 + -2x = 0

Solving
13 + -2x = 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 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {-1.111111111, 6.5}

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