6x^2=4(x+4)

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Solution for 6x^2=4(x+4) equation: 


Simplifying
6x2 = 4(x + 4)

Reorder the terms:
6x2 = 4(4 + x)
6x2 = (4 * 4 + x * 4)
6x2 = (16 + 4x)

Solving
6x2 = 16 + 4x

Solving for variable 'x'.

Reorder the terms:
-16 + -4x + 6x2 = 16 + 4x + -16 + -4x

Reorder the terms:
-16 + -4x + 6x2 = 16 + -16 + 4x + -4x

Combine like terms: 16 + -16 = 0
-16 + -4x + 6x2 = 0 + 4x + -4x
-16 + -4x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-16 + -4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + 3x2) = 0

Factor a trinomial.
2((-4 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 2}

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