(3x-4)(x+8)=4x(x+8)

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Solution for (3x-4)(x+8)=4x(x+8) equation: 


Simplifying
(3x + -4)(x + 8) = 4x(x + 8)

Reorder the terms:
(-4 + 3x)(x + 8) = 4x(x + 8)

Reorder the terms:
(-4 + 3x)(8 + x) = 4x(x + 8)

Multiply (-4 + 3x) * (8 + x)
(-4(8 + x) + 3x * (8 + x)) = 4x(x + 8)
((8 * -4 + x * -4) + 3x * (8 + x)) = 4x(x + 8)
((-32 + -4x) + 3x * (8 + x)) = 4x(x + 8)
(-32 + -4x + (8 * 3x + x * 3x)) = 4x(x + 8)
(-32 + -4x + (24x + 3x2)) = 4x(x + 8)

Combine like terms: -4x + 24x = 20x
(-32 + 20x + 3x2) = 4x(x + 8)

Reorder the terms:
-32 + 20x + 3x2 = 4x(8 + x)
-32 + 20x + 3x2 = (8 * 4x + x * 4x)
-32 + 20x + 3x2 = (32x + 4x2)

Solving
-32 + 20x + 3x2 = 32x + 4x2

Solving for variable 'x'.

Reorder the terms:
-32 + 20x + -32x + 3x2 + -4x2 = 32x + 4x2 + -32x + -4x2

Combine like terms: 20x + -32x = -12x
-32 + -12x + 3x2 + -4x2 = 32x + 4x2 + -32x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
-32 + -12x + -1x2 = 32x + 4x2 + -32x + -4x2

Reorder the terms:
-32 + -12x + -1x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-32 + -12x + -1x2 = 0 + 4x2 + -4x2
-32 + -12x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-32 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 12x + x2) = 0

Factor a trinomial.
-1((8 + x)(4 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

Simplifying
x = -8

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {-8, -4}

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