2x(x-4)=-23x+8

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Solution for 2x(x-4)=-23x+8 equation: 


Simplifying
2x(x + -4) = -23x + 8

Reorder the terms:
2x(-4 + x) = -23x + 8
(-4 * 2x + x * 2x) = -23x + 8
(-8x + 2x2) = -23x + 8

Reorder the terms:
-8x + 2x2 = 8 + -23x

Solving
-8x + 2x2 = 8 + -23x

Solving for variable 'x'.

Reorder the terms:
-8 + -8x + 23x + 2x2 = 8 + -23x + -8 + 23x

Combine like terms: -8x + 23x = 15x
-8 + 15x + 2x2 = 8 + -23x + -8 + 23x

Reorder the terms:
-8 + 15x + 2x2 = 8 + -8 + -23x + 23x

Combine like terms: 8 + -8 = 0
-8 + 15x + 2x2 = 0 + -23x + 23x
-8 + 15x + 2x2 = -23x + 23x

Combine like terms: -23x + 23x = 0
-8 + 15x + 2x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-8, 0.5}

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