(x+8)(x-4)=(2x+5)(x-4)

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Solution for (x+8)(x-4)=(2x+5)(x-4) equation: 


Simplifying
(x + 8)(x + -4) = (2x + 5)(x + -4)

Reorder the terms:
(8 + x)(x + -4) = (2x + 5)(x + -4)

Reorder the terms:
(8 + x)(-4 + x) = (2x + 5)(x + -4)

Multiply (8 + x) * (-4 + x)
(8(-4 + x) + x(-4 + x)) = (2x + 5)(x + -4)
((-4 * 8 + x * 8) + x(-4 + x)) = (2x + 5)(x + -4)
((-32 + 8x) + x(-4 + x)) = (2x + 5)(x + -4)
(-32 + 8x + (-4 * x + x * x)) = (2x + 5)(x + -4)
(-32 + 8x + (-4x + x2)) = (2x + 5)(x + -4)

Combine like terms: 8x + -4x = 4x
(-32 + 4x + x2) = (2x + 5)(x + -4)

Reorder the terms:
-32 + 4x + x2 = (5 + 2x)(x + -4)

Reorder the terms:
-32 + 4x + x2 = (5 + 2x)(-4 + x)

Multiply (5 + 2x) * (-4 + x)
-32 + 4x + x2 = (5(-4 + x) + 2x * (-4 + x))
-32 + 4x + x2 = ((-4 * 5 + x * 5) + 2x * (-4 + x))
-32 + 4x + x2 = ((-20 + 5x) + 2x * (-4 + x))
-32 + 4x + x2 = (-20 + 5x + (-4 * 2x + x * 2x))
-32 + 4x + x2 = (-20 + 5x + (-8x + 2x2))

Combine like terms: 5x + -8x = -3x
-32 + 4x + x2 = (-20 + -3x + 2x2)

Solving
-32 + 4x + x2 = -20 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + 20 + 4x + 3x + x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Combine like terms: -32 + 20 = -12
-12 + 4x + 3x + x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Combine like terms: 4x + 3x = 7x
-12 + 7x + x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-12 + 7x + -1x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Reorder the terms:
-12 + 7x + -1x2 = -20 + 20 + -3x + 3x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
-12 + 7x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
-12 + 7x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-12 + 7x + -1x2 = 0 + 2x2 + -2x2
-12 + 7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 7x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {4, 3}

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