3*x^2-8*x=30+x

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Solution for 3*x^2-8*x=30+x equation: 


Simplifying
3x2 + -8x = 30 + x

Reorder the terms:
-8x + 3x2 = 30 + x

Solving
-8x + 3x2 = 30 + x

Solving for variable 'x'.

Reorder the terms:
-30 + -8x + -1x + 3x2 = 30 + x + -30 + -1x

Combine like terms: -8x + -1x = -9x
-30 + -9x + 3x2 = 30 + x + -30 + -1x

Reorder the terms:
-30 + -9x + 3x2 = 30 + -30 + x + -1x

Combine like terms: 30 + -30 = 0
-30 + -9x + 3x2 = 0 + x + -1x
-30 + -9x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-30 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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