15x^2-85x+31=504x^2-297x-45

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Solution for 15x^2-85x+31=504x^2-297x-45 equation: 


Simplifying
15x2 + -85x + 31 = 504x2 + -297x + -45

Reorder the terms:
31 + -85x + 15x2 = 504x2 + -297x + -45

Reorder the terms:
31 + -85x + 15x2 = -45 + -297x + 504x2

Solving
31 + -85x + 15x2 = -45 + -297x + 504x2

Solving for variable 'x'.

Reorder the terms:
31 + 45 + -85x + 297x + 15x2 + -504x2 = -45 + -297x + 504x2 + 45 + 297x + -504x2

Combine like terms: 31 + 45 = 76
76 + -85x + 297x + 15x2 + -504x2 = -45 + -297x + 504x2 + 45 + 297x + -504x2

Combine like terms: -85x + 297x = 212x
76 + 212x + 15x2 + -504x2 = -45 + -297x + 504x2 + 45 + 297x + -504x2

Combine like terms: 15x2 + -504x2 = -489x2
76 + 212x + -489x2 = -45 + -297x + 504x2 + 45 + 297x + -504x2

Reorder the terms:
76 + 212x + -489x2 = -45 + 45 + -297x + 297x + 504x2 + -504x2

Combine like terms: -45 + 45 = 0
76 + 212x + -489x2 = 0 + -297x + 297x + 504x2 + -504x2
76 + 212x + -489x2 = -297x + 297x + 504x2 + -504x2

Combine like terms: -297x + 297x = 0
76 + 212x + -489x2 = 0 + 504x2 + -504x2
76 + 212x + -489x2 = 504x2 + -504x2

Combine like terms: 504x2 + -504x2 = 0
76 + 212x + -489x2 = 0

Factor a trinomial.
(2 + -3x)(38 + 163x) = 0


Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(38 + 163x)' equal to zero and attempt to solve:

Simplifying
38 + 163x = 0

Solving
38 + 163x = 0

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

Add '-38' to each side of the equation.
38 + -38 + 163x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 163x = 0 + -38
163x = 0 + -38

Combine like terms: 0 + -38 = -38
163x = -38

Divide each side by '163'.
x = -0.2331288344

Simplifying
x = -0.2331288344
Solution
x = {0.6666666667, -0.2331288344}

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