6x^2-15x=10x(2x-5)

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Solution for 6x^2-15x=10x(2x-5) equation:


Simplifying
6x2 + -15x = 10x(2x + -5)

Reorder the terms:
-15x + 6x2 = 10x(2x + -5)

Reorder the terms:
-15x + 6x2 = 10x(-5 + 2x)
-15x + 6x2 = (-5 * 10x + 2x * 10x)
-15x + 6x2 = (-50x + 20x2)

Solving
-15x + 6x2 = -50x + 20x2

Solving for variable 'x'.

Reorder the terms:
-15x + 50x + 6x2 + -20x2 = -50x + 20x2 + 50x + -20x2

Combine like terms: -15x + 50x = 35x
35x + 6x2 + -20x2 = -50x + 20x2 + 50x + -20x2

Combine like terms: 6x2 + -20x2 = -14x2
35x + -14x2 = -50x + 20x2 + 50x + -20x2

Reorder the terms:
35x + -14x2 = -50x + 50x + 20x2 + -20x2

Combine like terms: -50x + 50x = 0
35x + -14x2 = 0 + 20x2 + -20x2
35x + -14x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
35x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(5 + -2x) = 0

Ignore the factor 7.

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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