(2x+3)(x-8)=x(x-8)

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Solution for (2x+3)(x-8)=x(x-8) equation: 


Simplifying
(2x + 3)(x + -8) = x(x + -8)

Reorder the terms:
(3 + 2x)(x + -8) = x(x + -8)

Reorder the terms:
(3 + 2x)(-8 + x) = x(x + -8)

Multiply (3 + 2x) * (-8 + x)
(3(-8 + x) + 2x * (-8 + x)) = x(x + -8)
((-8 * 3 + x * 3) + 2x * (-8 + x)) = x(x + -8)
((-24 + 3x) + 2x * (-8 + x)) = x(x + -8)
(-24 + 3x + (-8 * 2x + x * 2x)) = x(x + -8)
(-24 + 3x + (-16x + 2x2)) = x(x + -8)

Combine like terms: 3x + -16x = -13x
(-24 + -13x + 2x2) = x(x + -8)

Reorder the terms:
-24 + -13x + 2x2 = x(-8 + x)
-24 + -13x + 2x2 = (-8 * x + x * x)
-24 + -13x + 2x2 = (-8x + x2)

Solving
-24 + -13x + 2x2 = -8x + x2

Solving for variable 'x'.

Reorder the terms:
-24 + -13x + 8x + 2x2 + -1x2 = -8x + x2 + 8x + -1x2

Combine like terms: -13x + 8x = -5x
-24 + -5x + 2x2 + -1x2 = -8x + x2 + 8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-24 + -5x + 1x2 = -8x + x2 + 8x + -1x2

Reorder the terms:
-24 + -5x + 1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-24 + -5x + 1x2 = 0 + x2 + -1x2
-24 + -5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + -5x + 1x2 = 0

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


Subproblem 1
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

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 = {-3, 8}

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