3x^2-30x+75=x-5

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Solution for 3x^2-30x+75=x-5 equation: 


Simplifying
3x2 + -30x + 75 = x + -5

Reorder the terms:
75 + -30x + 3x2 = x + -5

Reorder the terms:
75 + -30x + 3x2 = -5 + x

Solving
75 + -30x + 3x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
75 + 5 + -30x + -1x + 3x2 = -5 + x + 5 + -1x

Combine like terms: 75 + 5 = 80
80 + -30x + -1x + 3x2 = -5 + x + 5 + -1x

Combine like terms: -30x + -1x = -31x
80 + -31x + 3x2 = -5 + x + 5 + -1x

Reorder the terms:
80 + -31x + 3x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
80 + -31x + 3x2 = 0 + x + -1x
80 + -31x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
80 + -31x + 3x2 = 0

Factor a trinomial.
(5 + -1x)(16 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(16 + -3x)' equal to zero and attempt to solve:

Simplifying
16 + -3x = 0

Solving
16 + -3x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3x = 0 + -16
-3x = 0 + -16

Combine like terms: 0 + -16 = -16
-3x = -16

Divide each side by '-3'.
x = 5.333333333

Simplifying
x = 5.333333333
Solution
x = {5, 5.333333333}

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