8x(x-4)=10x^2-33x

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Solution for 8x(x-4)=10x^2-33x equation: 


Simplifying
8x(x + -4) = 10x2 + -33x

Reorder the terms:
8x(-4 + x) = 10x2 + -33x
(-4 * 8x + x * 8x) = 10x2 + -33x
(-32x + 8x2) = 10x2 + -33x

Reorder the terms:
-32x + 8x2 = -33x + 10x2

Solving
-32x + 8x2 = -33x + 10x2

Solving for variable 'x'.

Reorder the terms:
-32x + 33x + 8x2 + -10x2 = -33x + 10x2 + 33x + -10x2

Combine like terms: -32x + 33x = 1x
1x + 8x2 + -10x2 = -33x + 10x2 + 33x + -10x2

Combine like terms: 8x2 + -10x2 = -2x2
1x + -2x2 = -33x + 10x2 + 33x + -10x2

Reorder the terms:
1x + -2x2 = -33x + 33x + 10x2 + -10x2

Combine like terms: -33x + 33x = 0
1x + -2x2 = 0 + 10x2 + -10x2
1x + -2x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
1x + -2x2 = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 0.5}

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