5x(2x+9)=10x(2+3x)

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Solution for 5x(2x+9)=10x(2+3x) equation: 


Simplifying
5x(2x + 9) = 10x(2 + 3x)

Reorder the terms:
5x(9 + 2x) = 10x(2 + 3x)
(9 * 5x + 2x * 5x) = 10x(2 + 3x)
(45x + 10x2) = 10x(2 + 3x)
45x + 10x2 = (2 * 10x + 3x * 10x)
45x + 10x2 = (20x + 30x2)

Solving
45x + 10x2 = 20x + 30x2

Solving for variable 'x'.

Reorder the terms:
45x + -20x + 10x2 + -30x2 = 20x + 30x2 + -20x + -30x2

Combine like terms: 45x + -20x = 25x
25x + 10x2 + -30x2 = 20x + 30x2 + -20x + -30x2

Combine like terms: 10x2 + -30x2 = -20x2
25x + -20x2 = 20x + 30x2 + -20x + -30x2

Reorder the terms:
25x + -20x2 = 20x + -20x + 30x2 + -30x2

Combine like terms: 20x + -20x = 0
25x + -20x2 = 0 + 30x2 + -30x2
25x + -20x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
25x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(5 + -4x) = 0

Ignore the factor 5.

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 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0, 1.25}

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