2x(8x+1)=x(15x+10)

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Solution for 2x(8x+1)=x(15x+10) equation: 


Simplifying
2x(8x + 1) = x(15x + 10)

Reorder the terms:
2x(1 + 8x) = x(15x + 10)
(1 * 2x + 8x * 2x) = x(15x + 10)
(2x + 16x2) = x(15x + 10)

Reorder the terms:
2x + 16x2 = x(10 + 15x)
2x + 16x2 = (10 * x + 15x * x)
2x + 16x2 = (10x + 15x2)

Solving
2x + 16x2 = 10x + 15x2

Solving for variable 'x'.

Reorder the terms:
2x + -10x + 16x2 + -15x2 = 10x + 15x2 + -10x + -15x2

Combine like terms: 2x + -10x = -8x
-8x + 16x2 + -15x2 = 10x + 15x2 + -10x + -15x2

Combine like terms: 16x2 + -15x2 = 1x2
-8x + 1x2 = 10x + 15x2 + -10x + -15x2

Reorder the terms:
-8x + 1x2 = 10x + -10x + 15x2 + -15x2

Combine like terms: 10x + -10x = 0
-8x + 1x2 = 0 + 15x2 + -15x2
-8x + 1x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + x) = 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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

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

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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