6x(x+4)=(2x+4)(x+4)

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


Simplifying
6x(x + 4) = (2x + 4)(x + 4)

Reorder the terms:
6x(4 + x) = (2x + 4)(x + 4)
(4 * 6x + x * 6x) = (2x + 4)(x + 4)
(24x + 6x2) = (2x + 4)(x + 4)

Reorder the terms:
24x + 6x2 = (4 + 2x)(x + 4)

Reorder the terms:
24x + 6x2 = (4 + 2x)(4 + x)

Multiply (4 + 2x) * (4 + x)
24x + 6x2 = (4(4 + x) + 2x * (4 + x))
24x + 6x2 = ((4 * 4 + x * 4) + 2x * (4 + x))
24x + 6x2 = ((16 + 4x) + 2x * (4 + x))
24x + 6x2 = (16 + 4x + (4 * 2x + x * 2x))
24x + 6x2 = (16 + 4x + (8x + 2x2))

Combine like terms: 4x + 8x = 12x
24x + 6x2 = (16 + 12x + 2x2)

Solving
24x + 6x2 = 16 + 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + 24x + -12x + 6x2 + -2x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Combine like terms: 24x + -12x = 12x
-16 + 12x + 6x2 + -2x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-16 + 12x + 4x2 = 16 + 12x + 2x2 + -16 + -12x + -2x2

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

Combine like terms: 16 + -16 = 0
-16 + 12x + 4x2 = 0 + 12x + -12x + 2x2 + -2x2
-16 + 12x + 4x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-16 + 12x + 4x2 = 0 + 2x2 + -2x2
-16 + 12x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-16 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1}

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