x(4-x)=(2x+3)(x-2)+8

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Solution for x(4-x)=(2x+3)(x-2)+8 equation: 


Simplifying
x(4 + -1x) = (2x + 3)(x + -2) + 8
(4 * x + -1x * x) = (2x + 3)(x + -2) + 8
(4x + -1x2) = (2x + 3)(x + -2) + 8

Reorder the terms:
4x + -1x2 = (3 + 2x)(x + -2) + 8

Reorder the terms:
4x + -1x2 = (3 + 2x)(-2 + x) + 8

Multiply (3 + 2x) * (-2 + x)
4x + -1x2 = (3(-2 + x) + 2x * (-2 + x)) + 8
4x + -1x2 = ((-2 * 3 + x * 3) + 2x * (-2 + x)) + 8
4x + -1x2 = ((-6 + 3x) + 2x * (-2 + x)) + 8
4x + -1x2 = (-6 + 3x + (-2 * 2x + x * 2x)) + 8
4x + -1x2 = (-6 + 3x + (-4x + 2x2)) + 8

Combine like terms: 3x + -4x = -1x
4x + -1x2 = (-6 + -1x + 2x2) + 8

Reorder the terms:
4x + -1x2 = -6 + 8 + -1x + 2x2

Combine like terms: -6 + 8 = 2
4x + -1x2 = 2 + -1x + 2x2

Solving
4x + -1x2 = 2 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 4x + x + -1x2 + -2x2 = 2 + -1x + 2x2 + -2 + x + -2x2

Combine like terms: 4x + x = 5x
-2 + 5x + -1x2 + -2x2 = 2 + -1x + 2x2 + -2 + x + -2x2

Combine like terms: -1x2 + -2x2 = -3x2
-2 + 5x + -3x2 = 2 + -1x + 2x2 + -2 + x + -2x2

Reorder the terms:
-2 + 5x + -3x2 = 2 + -2 + -1x + x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
-2 + 5x + -3x2 = 0 + -1x + x + 2x2 + -2x2
-2 + 5x + -3x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-2 + 5x + -3x2 = 0 + 2x2 + -2x2
-2 + 5x + -3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + 5x + -3x2 = 0

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


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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {1, 0.6666666667}

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