3x^2-31x+75=x-5

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Solution for 3x^2-31x+75=x-5 equation: 


Simplifying
3x2 + -31x + 75 = x + -5

Reorder the terms:
75 + -31x + 3x2 = x + -5

Reorder the terms:
75 + -31x + 3x2 = -5 + x

Solving
75 + -31x + 3x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
75 + 5 + -31x + -1x + 3x2 = -5 + x + 5 + -1x

Combine like terms: 75 + 5 = 80
80 + -31x + -1x + 3x2 = -5 + x + 5 + -1x

Combine like terms: -31x + -1x = -32x
80 + -32x + 3x2 = -5 + x + 5 + -1x

Reorder the terms:
80 + -32x + 3x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
80 + -32x + 3x2 = 0 + x + -1x
80 + -32x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
80 + -32x + 3x2 = 0

Factor a trinomial.
(4 + -1x)(20 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(20 + -3x)' equal to zero and attempt to solve:

Simplifying
20 + -3x = 0

Solving
20 + -3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3x = 0 + -20
-3x = 0 + -20

Combine like terms: 0 + -20 = -20
-3x = -20

Divide each side by '-3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {4, 6.666666667}

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