3x^2-16=2-3x

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Solution for 3x^2-16=2-3x equation: 


Simplifying
3x2 + -16 = 2 + -3x

Reorder the terms:
-16 + 3x2 = 2 + -3x

Solving
-16 + 3x2 = 2 + -3x

Solving for variable 'x'.

Reorder the terms:
-16 + -2 + 3x + 3x2 = 2 + -3x + -2 + 3x

Combine like terms: -16 + -2 = -18
-18 + 3x + 3x2 = 2 + -3x + -2 + 3x

Reorder the terms:
-18 + 3x + 3x2 = 2 + -2 + -3x + 3x

Combine like terms: 2 + -2 = 0
-18 + 3x + 3x2 = 0 + -3x + 3x
-18 + 3x + 3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-18 + 3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + x + x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 2}

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