x^2+32x=9x^2+24x

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Solution for x^2+32x=9x^2+24x equation:


Simplifying
x2 + 32x = 9x2 + 24x

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

Reorder the terms:
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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