15x^2=16x^2-32x

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Solution for 15x^2=16x^2-32x equation:


Simplifying
15x2 = 16x2 + -32x

Reorder the terms:
15x2 = -32x + 16x2

Solving
15x2 = -32x + 16x2

Solving for variable 'x'.

Reorder the terms:
32x + 15x2 + -16x2 = -32x + 16x2 + 32x + -16x2

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

Reorder the terms:
32x + -1x2 = -32x + 32x + 16x2 + -16x2

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(32 + -1x) = 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 '(32 + -1x)' equal to zero and attempt to solve: Simplifying 32 + -1x = 0 Solving 32 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -1x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 0 + -32 -1x = 0 + -32 Combine like terms: 0 + -32 = -32 -1x = -32 Divide each side by '-1'. x = 32 Simplifying x = 32

Solution

x = {0, 32}

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