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

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


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

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

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

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

Multiply (-7 + 2x) * (-5 + x)
-15x + 3x2 = (-7(-5 + x) + 2x * (-5 + x))
-15x + 3x2 = ((-5 * -7 + x * -7) + 2x * (-5 + x))
-15x + 3x2 = ((35 + -7x) + 2x * (-5 + x))
-15x + 3x2 = (35 + -7x + (-5 * 2x + x * 2x))
-15x + 3x2 = (35 + -7x + (-10x + 2x2))

Combine like terms: -7x + -10x = -17x
-15x + 3x2 = (35 + -17x + 2x2)

Solving
-15x + 3x2 = 35 + -17x + 2x2

Solving for variable 'x'.

Reorder the terms:
-35 + -15x + 17x + 3x2 + -2x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Combine like terms: -15x + 17x = 2x
-35 + 2x + 3x2 + -2x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-35 + 2x + 1x2 = 35 + -17x + 2x2 + -35 + 17x + -2x2

Reorder the terms:
-35 + 2x + 1x2 = 35 + -35 + -17x + 17x + 2x2 + -2x2

Combine like terms: 35 + -35 = 0
-35 + 2x + 1x2 = 0 + -17x + 17x + 2x2 + -2x2
-35 + 2x + 1x2 = -17x + 17x + 2x2 + -2x2

Combine like terms: -17x + 17x = 0
-35 + 2x + 1x2 = 0 + 2x2 + -2x2
-35 + 2x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-35 + 2x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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