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

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

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

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

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

Solving
-15x + 3x2 = -14x + 2x2

Solving for variable 'x'.

Reorder the terms:
-15x + 14x + 3x2 + -2x2 = -14x + 2x2 + 14x + -2x2

Combine like terms: -15x + 14x = -1x
-1x + 3x2 + -2x2 = -14x + 2x2 + 14x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-1x + 1x2 = -14x + 2x2 + 14x + -2x2

Reorder the terms:
-1x + 1x2 = -14x + 14x + 2x2 + -2x2

Combine like terms: -14x + 14x = 0
-1x + 1x2 = 0 + 2x2 + -2x2
-1x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}