3x^2-17x+10=-6-5x+x^2

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Solution for 3x^2-17x+10=-6-5x+x^2 equation: 


Simplifying
3x2 + -17x + 10 = -6 + -5x + x2

Reorder the terms:
10 + -17x + 3x2 = -6 + -5x + x2

Solving
10 + -17x + 3x2 = -6 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
10 + 6 + -17x + 5x + 3x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2

Combine like terms: 10 + 6 = 16
16 + -17x + 5x + 3x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2

Combine like terms: -17x + 5x = -12x
16 + -12x + 3x2 + -1x2 = -6 + -5x + x2 + 6 + 5x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
16 + -12x + 2x2 = -6 + -5x + x2 + 6 + 5x + -1x2

Reorder the terms:
16 + -12x + 2x2 = -6 + 6 + -5x + 5x + x2 + -1x2

Combine like terms: -6 + 6 = 0
16 + -12x + 2x2 = 0 + -5x + 5x + x2 + -1x2
16 + -12x + 2x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
16 + -12x + 2x2 = 0 + x2 + -1x2
16 + -12x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -6x + x2) = 0

Factor a trinomial.
2((2 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(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
Solution
x = {2, 4}

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