6*x^2+8*x=3*x^2+15*x

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Solution for 6*x^2+8*x=3*x^2+15*x equation: 


Simplifying
6x2 + 8x = 3x2 + 15x

Reorder the terms:
8x + 6x2 = 3x2 + 15x

Reorder the terms:
8x + 6x2 = 15x + 3x2

Solving
8x + 6x2 = 15x + 3x2

Solving for variable 'x'.

Reorder the terms:
8x + -15x + 6x2 + -3x2 = 15x + 3x2 + -15x + -3x2

Combine like terms: 8x + -15x = -7x
-7x + 6x2 + -3x2 = 15x + 3x2 + -15x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
-7x + 3x2 = 15x + 3x2 + -15x + -3x2

Reorder the terms:
-7x + 3x2 = 15x + -15x + 3x2 + -3x2

Combine like terms: 15x + -15x = 0
-7x + 3x2 = 0 + 3x2 + -3x2
-7x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-7x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 3x) = 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 '(-7 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, 2.333333333}

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