0=38x-12x^2-16

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Solution for 0=38x-12x^2-16 equation:


Simplifying
0 = 38x + -12x2 + -16

Reorder the terms:
0 = -16 + 38x + -12x2

Solving
0 = -16 + 38x + -12x2

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -38x + 12x2 = -16 + 38x + -12x2 + 16 + -38x + 12x2

Reorder the terms:
16 + -38x + 12x2 = -16 + 16 + 38x + -38x + -12x2 + 12x2

Combine like terms: -16 + 16 = 0
16 + -38x + 12x2 = 0 + 38x + -38x + -12x2 + 12x2
16 + -38x + 12x2 = 38x + -38x + -12x2 + 12x2

Combine like terms: 38x + -38x = 0
16 + -38x + 12x2 = 0 + -12x2 + 12x2
16 + -38x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
16 + -38x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -19x + 6x2) = 0

Factor a trinomial.
2((1 + -2x)(8 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0.5, 2.666666667}

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