(2x+8)(x-1)=21x

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Solution for (2x+8)(x-1)=21x equation: 


Simplifying
(2x + 8)(x + -1) = 21x

Reorder the terms:
(8 + 2x)(x + -1) = 21x

Reorder the terms:
(8 + 2x)(-1 + x) = 21x

Multiply (8 + 2x) * (-1 + x)
(8(-1 + x) + 2x * (-1 + x)) = 21x
((-1 * 8 + x * 8) + 2x * (-1 + x)) = 21x
((-8 + 8x) + 2x * (-1 + x)) = 21x
(-8 + 8x + (-1 * 2x + x * 2x)) = 21x
(-8 + 8x + (-2x + 2x2)) = 21x

Combine like terms: 8x + -2x = 6x
(-8 + 6x + 2x2) = 21x

Solving
-8 + 6x + 2x2 = 21x

Solving for variable 'x'.

Reorder the terms:
-8 + 6x + -21x + 2x2 = 21x + -21x

Combine like terms: 6x + -21x = -15x
-8 + -15x + 2x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-8 + -15x + 2x2 = 0

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


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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
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
Solution
x = {-0.5, 8}

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