x(32+x)=3x(3x+8)

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Solution for x(32+x)=3x(3x+8) equation: 


Simplifying
x(32 + x) = 3x(3x + 8)
(32 * x + x * x) = 3x(3x + 8)
(32x + x2) = 3x(3x + 8)

Reorder the terms:
32x + x2 = 3x(8 + 3x)
32x + x2 = (8 * 3x + 3x * 3x)
32x + x2 = (24x + 9x2)

Solving
32x + x2 = 24x + 9x2

Solving for variable 'x'.

Reorder the terms:
32x + -24x + x2 + -9x2 = 24x + 9x2 + -24x + -9x2

Combine like terms: 32x + -24x = 8x
8x + x2 + -9x2 = 24x + 9x2 + -24x + -9x2

Combine like terms: x2 + -9x2 = -8x2
8x + -8x2 = 24x + 9x2 + -24x + -9x2

Reorder the terms:
8x + -8x2 = 24x + -24x + 9x2 + -9x2

Combine like terms: 24x + -24x = 0
8x + -8x2 = 0 + 9x2 + -9x2
8x + -8x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
8x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8x'.
8x(1 + -1x) = 0

Ignore the factor 8.

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 + -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 = {0, 1}

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