20x^2+x^2=(x+16)x^2

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Solution for 20x^2+x^2=(x+16)x^2 equation:


Simplifying
20x2 + x2 = (x + 16) * x2

Combine like terms: 20x2 + x2 = 21x2
21x2 = (x + 16) * x2

Reorder the terms:
21x2 = (16 + x) * x2

Reorder the terms for easier multiplication:
21x2 = x2(16 + x)
21x2 = (16 * x2 + x * x2)
21x2 = (16x2 + x3)

Solving
21x2 = 16x2 + x3

Solving for variable 'x'.

Combine like terms: 21x2 + -16x2 = 5x2
5x2 + -1x3 = 16x2 + x3 + -16x2 + -1x3

Reorder the terms:
5x2 + -1x3 = 16x2 + -16x2 + x3 + -1x3

Combine like terms: 16x2 + -16x2 = 0
5x2 + -1x3 = 0 + x3 + -1x3
5x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
5x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(5 + -1x) = 0

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {0, 5}

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