12x^2+3x-16=5-4x-2x^2

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Solution for 12x^2+3x-16=5-4x-2x^2 equation: 


Simplifying
12x2 + 3x + -16 = 5 + -4x + -2x2

Reorder the terms:
-16 + 3x + 12x2 = 5 + -4x + -2x2

Solving
-16 + 3x + 12x2 = 5 + -4x + -2x2

Solving for variable 'x'.

Reorder the terms:
-16 + -5 + 3x + 4x + 12x2 + 2x2 = 5 + -4x + -2x2 + -5 + 4x + 2x2

Combine like terms: -16 + -5 = -21
-21 + 3x + 4x + 12x2 + 2x2 = 5 + -4x + -2x2 + -5 + 4x + 2x2

Combine like terms: 3x + 4x = 7x
-21 + 7x + 12x2 + 2x2 = 5 + -4x + -2x2 + -5 + 4x + 2x2

Combine like terms: 12x2 + 2x2 = 14x2
-21 + 7x + 14x2 = 5 + -4x + -2x2 + -5 + 4x + 2x2

Reorder the terms:
-21 + 7x + 14x2 = 5 + -5 + -4x + 4x + -2x2 + 2x2

Combine like terms: 5 + -5 = 0
-21 + 7x + 14x2 = 0 + -4x + 4x + -2x2 + 2x2
-21 + 7x + 14x2 = -4x + 4x + -2x2 + 2x2

Combine like terms: -4x + 4x = 0
-21 + 7x + 14x2 = 0 + -2x2 + 2x2
-21 + 7x + 14x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-21 + 7x + 14x2 = 0

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

Factor a trinomial.
7((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 7.

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

Simplifying
-3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 1}

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