(x-8)(4x+2)=10x(x-8)

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Solution for (x-8)(4x+2)=10x(x-8) equation: 


Simplifying
(x + -8)(4x + 2) = 10x(x + -8)

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

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

Multiply (-8 + x) * (2 + 4x)
(-8(2 + 4x) + x(2 + 4x)) = 10x(x + -8)
((2 * -8 + 4x * -8) + x(2 + 4x)) = 10x(x + -8)
((-16 + -32x) + x(2 + 4x)) = 10x(x + -8)
(-16 + -32x + (2 * x + 4x * x)) = 10x(x + -8)
(-16 + -32x + (2x + 4x2)) = 10x(x + -8)

Combine like terms: -32x + 2x = -30x
(-16 + -30x + 4x2) = 10x(x + -8)

Reorder the terms:
-16 + -30x + 4x2 = 10x(-8 + x)
-16 + -30x + 4x2 = (-8 * 10x + x * 10x)
-16 + -30x + 4x2 = (-80x + 10x2)

Solving
-16 + -30x + 4x2 = -80x + 10x2

Solving for variable 'x'.

Reorder the terms:
-16 + -30x + 80x + 4x2 + -10x2 = -80x + 10x2 + 80x + -10x2

Combine like terms: -30x + 80x = 50x
-16 + 50x + 4x2 + -10x2 = -80x + 10x2 + 80x + -10x2

Combine like terms: 4x2 + -10x2 = -6x2
-16 + 50x + -6x2 = -80x + 10x2 + 80x + -10x2

Reorder the terms:
-16 + 50x + -6x2 = -80x + 80x + 10x2 + -10x2

Combine like terms: -80x + 80x = 0
-16 + 50x + -6x2 = 0 + 10x2 + -10x2
-16 + 50x + -6x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-16 + 50x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 25x + -3x2) = 0

Factor a trinomial.
2((-8 + x)(1 + -3x)) = 0

Ignore the factor 2.

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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {8, 0.3333333333}

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