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

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


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

Reorder the terms:
5x(-3 + x) = 5x(9 + -2)
(-3 * 5x + x * 5x) = 5x(9 + -2)
(-15x + 5x2) = 5x(9 + -2)

Combine like terms: 9 + -2 = 7
-15x + 5x2 = 5x(7)

Reorder the terms for easier multiplication:
-15x + 5x2 = 5 * 7x

Multiply 5 * 7
-15x + 5x2 = 35x

Solving
-15x + 5x2 = 35x

Solving for variable 'x'.

Reorder the terms:
-15x + -35x + 5x2 = 35x + -35x

Combine like terms: -15x + -35x = -50x
-50x + 5x2 = 35x + -35x

Combine like terms: 35x + -35x = 0
-50x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-10 + x) = 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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, 10}

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