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

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Solution for 5(x+4)=(x-3)(x+4) equation: 


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

Reorder the terms:
5(4 + x) = (x + -3)(x + 4)
(4 * 5 + x * 5) = (x + -3)(x + 4)
(20 + 5x) = (x + -3)(x + 4)

Reorder the terms:
20 + 5x = (-3 + x)(x + 4)

Reorder the terms:
20 + 5x = (-3 + x)(4 + x)

Multiply (-3 + x) * (4 + x)
20 + 5x = (-3(4 + x) + x(4 + x))
20 + 5x = ((4 * -3 + x * -3) + x(4 + x))
20 + 5x = ((-12 + -3x) + x(4 + x))
20 + 5x = (-12 + -3x + (4 * x + x * x))
20 + 5x = (-12 + -3x + (4x + x2))

Combine like terms: -3x + 4x = 1x
20 + 5x = (-12 + 1x + x2)

Solving
20 + 5x = -12 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
20 + 12 + 5x + -1x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

Combine like terms: 20 + 12 = 32
32 + 5x + -1x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

Combine like terms: 5x + -1x = 4x
32 + 4x + -1x2 = -12 + 1x + x2 + 12 + -1x + -1x2

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

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

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

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

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


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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
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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