7x(2x-5)=3x(2-5x)

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Solution for 7x(2x-5)=3x(2-5x) equation: 


Simplifying
7x(2x + -5) = 3x(2 + -5x)

Reorder the terms:
7x(-5 + 2x) = 3x(2 + -5x)
(-5 * 7x + 2x * 7x) = 3x(2 + -5x)
(-35x + 14x2) = 3x(2 + -5x)
-35x + 14x2 = (2 * 3x + -5x * 3x)
-35x + 14x2 = (6x + -15x2)

Solving
-35x + 14x2 = 6x + -15x2

Solving for variable 'x'.

Reorder the terms:
-35x + -6x + 14x2 + 15x2 = 6x + -15x2 + -6x + 15x2

Combine like terms: -35x + -6x = -41x
-41x + 14x2 + 15x2 = 6x + -15x2 + -6x + 15x2

Combine like terms: 14x2 + 15x2 = 29x2
-41x + 29x2 = 6x + -15x2 + -6x + 15x2

Reorder the terms:
-41x + 29x2 = 6x + -6x + -15x2 + 15x2

Combine like terms: 6x + -6x = 0
-41x + 29x2 = 0 + -15x2 + 15x2
-41x + 29x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
-41x + 29x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-41 + 29x) = 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 '(-41 + 29x)' equal to zero and attempt to solve:

Simplifying
-41 + 29x = 0

Solving
-41 + 29x = 0

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

Add '41' to each side of the equation.
-41 + 41 + 29x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 29x = 0 + 41
29x = 0 + 41

Combine like terms: 0 + 41 = 41
29x = 41

Divide each side by '29'.
x = 1.413793103

Simplifying
x = 1.413793103
Solution
x = {0, 1.413793103}

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