(5x-8)(4-3x)+x(4-x)=0

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Solution for (5x-8)(4-3x)+x(4-x)=0 equation:


Simplifying
(5x + -8)(4 + -3x) + x(4 + -1x) = 0

Reorder the terms:
(-8 + 5x)(4 + -3x) + x(4 + -1x) = 0

Multiply (-8 + 5x) * (4 + -3x)
(-8(4 + -3x) + 5x * (4 + -3x)) + x(4 + -1x) = 0
((4 * -8 + -3x * -8) + 5x * (4 + -3x)) + x(4 + -1x) = 0
((-32 + 24x) + 5x * (4 + -3x)) + x(4 + -1x) = 0
(-32 + 24x + (4 * 5x + -3x * 5x)) + x(4 + -1x) = 0
(-32 + 24x + (20x + -15x2)) + x(4 + -1x) = 0

Combine like terms: 24x + 20x = 44x
(-32 + 44x + -15x2) + x(4 + -1x) = 0
-32 + 44x + -15x2 + (4 * x + -1x * x) = 0
-32 + 44x + -15x2 + (4x + -1x2) = 0

Reorder the terms:
-32 + 44x + 4x + -15x2 + -1x2 = 0

Combine like terms: 44x + 4x = 48x
-32 + 48x + -15x2 + -1x2 = 0

Combine like terms: -15x2 + -1x2 = -16x2
-32 + 48x + -16x2 = 0

Solving
-32 + 48x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + 3x + -1x2) = 0

Factor a trinomial.
16((-2 + x)(1 + -1x)) = 0

Ignore the factor 16.

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

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {2, 1}

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