(3x-2)(x+4)=2(x+1)(2x-4)

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Solution for (3x-2)(x+4)=2(x+1)(2x-4) equation:


Simplifying
(3x + -2)(x + 4) = 2(x + 1)(2x + -4)

Reorder the terms:
(-2 + 3x)(x + 4) = 2(x + 1)(2x + -4)

Reorder the terms:
(-2 + 3x)(4 + x) = 2(x + 1)(2x + -4)

Multiply (-2 + 3x) * (4 + x)
(-2(4 + x) + 3x * (4 + x)) = 2(x + 1)(2x + -4)
((4 * -2 + x * -2) + 3x * (4 + x)) = 2(x + 1)(2x + -4)
((-8 + -2x) + 3x * (4 + x)) = 2(x + 1)(2x + -4)
(-8 + -2x + (4 * 3x + x * 3x)) = 2(x + 1)(2x + -4)
(-8 + -2x + (12x + 3x2)) = 2(x + 1)(2x + -4)

Combine like terms: -2x + 12x = 10x
(-8 + 10x + 3x2) = 2(x + 1)(2x + -4)

Reorder the terms:
-8 + 10x + 3x2 = 2(1 + x)(2x + -4)

Reorder the terms:
-8 + 10x + 3x2 = 2(1 + x)(-4 + 2x)

Multiply (1 + x) * (-4 + 2x)
-8 + 10x + 3x2 = 2(1(-4 + 2x) + x(-4 + 2x))
-8 + 10x + 3x2 = 2((-4 * 1 + 2x * 1) + x(-4 + 2x))
-8 + 10x + 3x2 = 2((-4 + 2x) + x(-4 + 2x))
-8 + 10x + 3x2 = 2(-4 + 2x + (-4 * x + 2x * x))
-8 + 10x + 3x2 = 2(-4 + 2x + (-4x + 2x2))

Combine like terms: 2x + -4x = -2x
-8 + 10x + 3x2 = 2(-4 + -2x + 2x2)
-8 + 10x + 3x2 = (-4 * 2 + -2x * 2 + 2x2 * 2)
-8 + 10x + 3x2 = (-8 + -4x + 4x2)

Add '8' to each side of the equation.
-8 + 10x + 8 + 3x2 = -8 + -4x + 8 + 4x2

Reorder the terms:
-8 + 8 + 10x + 3x2 = -8 + -4x + 8 + 4x2

Combine like terms: -8 + 8 = 0
0 + 10x + 3x2 = -8 + -4x + 8 + 4x2
10x + 3x2 = -8 + -4x + 8 + 4x2

Reorder the terms:
10x + 3x2 = -8 + 8 + -4x + 4x2

Combine like terms: -8 + 8 = 0
10x + 3x2 = 0 + -4x + 4x2
10x + 3x2 = -4x + 4x2

Solving
10x + 3x2 = -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
10x + 4x + 3x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 10x + 4x = 14x
14x + 3x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
14x + -1x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
14x + -1x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
14x + -1x2 = 0 + 4x2 + -4x2
14x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(14 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {0, 14}

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