2x(9-5x)=5x(2-3x)

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


Simplifying
2x(9 + -5x) = 5x(2 + -3x)
(9 * 2x + -5x * 2x) = 5x(2 + -3x)
(18x + -10x2) = 5x(2 + -3x)
18x + -10x2 = (2 * 5x + -3x * 5x)
18x + -10x2 = (10x + -15x2)

Solving
18x + -10x2 = 10x + -15x2

Solving for variable 'x'.

Reorder the terms:
18x + -10x + -10x2 + 15x2 = 10x + -15x2 + -10x + 15x2

Combine like terms: 18x + -10x = 8x
8x + -10x2 + 15x2 = 10x + -15x2 + -10x + 15x2

Combine like terms: -10x2 + 15x2 = 5x2
8x + 5x2 = 10x + -15x2 + -10x + 15x2

Reorder the terms:
8x + 5x2 = 10x + -10x + -15x2 + 15x2

Combine like terms: 10x + -10x = 0
8x + 5x2 = 0 + -15x2 + 15x2
8x + 5x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
8x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 5x) = 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 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 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 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
Solution
x = {0, -1.6}

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