7x(x-4)=(2x+8)(x-4)

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Solution for 7x(x-4)=(2x+8)(x-4) equation: 


Simplifying
7x(x + -4) = (2x + 8)(x + -4)

Reorder the terms:
7x(-4 + x) = (2x + 8)(x + -4)
(-4 * 7x + x * 7x) = (2x + 8)(x + -4)
(-28x + 7x2) = (2x + 8)(x + -4)

Reorder the terms:
-28x + 7x2 = (8 + 2x)(x + -4)

Reorder the terms:
-28x + 7x2 = (8 + 2x)(-4 + x)

Multiply (8 + 2x) * (-4 + x)
-28x + 7x2 = (8(-4 + x) + 2x * (-4 + x))
-28x + 7x2 = ((-4 * 8 + x * 8) + 2x * (-4 + x))
-28x + 7x2 = ((-32 + 8x) + 2x * (-4 + x))
-28x + 7x2 = (-32 + 8x + (-4 * 2x + x * 2x))
-28x + 7x2 = (-32 + 8x + (-8x + 2x2))

Combine like terms: 8x + -8x = 0
-28x + 7x2 = (-32 + 0 + 2x2)
-28x + 7x2 = (-32 + 2x2)

Solving
-28x + 7x2 = -32 + 2x2

Solving for variable 'x'.

Reorder the terms:
32 + -28x + 7x2 + -2x2 = -32 + 2x2 + 32 + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
32 + -28x + 5x2 = -32 + 2x2 + 32 + -2x2

Reorder the terms:
32 + -28x + 5x2 = -32 + 32 + 2x2 + -2x2

Combine like terms: -32 + 32 = 0
32 + -28x + 5x2 = 0 + 2x2 + -2x2
32 + -28x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + -28x + 5x2 = 0

Factor a trinomial.
(8 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6

Subproblem 2
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
Solution
x = {1.6, 4}

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