6x^2-17x-14=-3x+6

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Solution for 6x^2-17x-14=-3x+6 equation: 


Simplifying
6x2 + -17x + -14 = -3x + 6

Reorder the terms:
-14 + -17x + 6x2 = -3x + 6

Reorder the terms:
-14 + -17x + 6x2 = 6 + -3x

Solving
-14 + -17x + 6x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
-14 + -6 + -17x + 3x + 6x2 = 6 + -3x + -6 + 3x

Combine like terms: -14 + -6 = -20
-20 + -17x + 3x + 6x2 = 6 + -3x + -6 + 3x

Combine like terms: -17x + 3x = -14x
-20 + -14x + 6x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-20 + -14x + 6x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-20 + -14x + 6x2 = 0 + -3x + 3x
-20 + -14x + 6x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-20 + -14x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -7x + 3x2) = 0

Factor a trinomial.
2((-1 + -1x)(10 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {-1, 3.333333333}

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