4x(x-5)=(3x-7)(x-5)

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Solution for 4x(x-5)=(3x-7)(x-5) equation: 


Simplifying
4x(x + -5) = (3x + -7)(x + -5)

Reorder the terms:
4x(-5 + x) = (3x + -7)(x + -5)
(-5 * 4x + x * 4x) = (3x + -7)(x + -5)
(-20x + 4x2) = (3x + -7)(x + -5)

Reorder the terms:
-20x + 4x2 = (-7 + 3x)(x + -5)

Reorder the terms:
-20x + 4x2 = (-7 + 3x)(-5 + x)

Multiply (-7 + 3x) * (-5 + x)
-20x + 4x2 = (-7(-5 + x) + 3x * (-5 + x))
-20x + 4x2 = ((-5 * -7 + x * -7) + 3x * (-5 + x))
-20x + 4x2 = ((35 + -7x) + 3x * (-5 + x))
-20x + 4x2 = (35 + -7x + (-5 * 3x + x * 3x))
-20x + 4x2 = (35 + -7x + (-15x + 3x2))

Combine like terms: -7x + -15x = -22x
-20x + 4x2 = (35 + -22x + 3x2)

Solving
-20x + 4x2 = 35 + -22x + 3x2

Solving for variable 'x'.

Reorder the terms:
-35 + -20x + 22x + 4x2 + -3x2 = 35 + -22x + 3x2 + -35 + 22x + -3x2

Combine like terms: -20x + 22x = 2x
-35 + 2x + 4x2 + -3x2 = 35 + -22x + 3x2 + -35 + 22x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-35 + 2x + 1x2 = 35 + -22x + 3x2 + -35 + 22x + -3x2

Reorder the terms:
-35 + 2x + 1x2 = 35 + -35 + -22x + 22x + 3x2 + -3x2

Combine like terms: 35 + -35 = 0
-35 + 2x + 1x2 = 0 + -22x + 22x + 3x2 + -3x2
-35 + 2x + 1x2 = -22x + 22x + 3x2 + -3x2

Combine like terms: -22x + 22x = 0
-35 + 2x + 1x2 = 0 + 3x2 + -3x2
-35 + 2x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 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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