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

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


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

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

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

Multiply (-7 + x) * (-5 + 3x)
(-7(-5 + 3x) + x(-5 + 3x)) = (x + -7)(7x + 5)
((-5 * -7 + 3x * -7) + x(-5 + 3x)) = (x + -7)(7x + 5)
((35 + -21x) + x(-5 + 3x)) = (x + -7)(7x + 5)
(35 + -21x + (-5 * x + 3x * x)) = (x + -7)(7x + 5)
(35 + -21x + (-5x + 3x2)) = (x + -7)(7x + 5)

Combine like terms: -21x + -5x = -26x
(35 + -26x + 3x2) = (x + -7)(7x + 5)

Reorder the terms:
35 + -26x + 3x2 = (-7 + x)(7x + 5)

Reorder the terms:
35 + -26x + 3x2 = (-7 + x)(5 + 7x)

Multiply (-7 + x) * (5 + 7x)
35 + -26x + 3x2 = (-7(5 + 7x) + x(5 + 7x))
35 + -26x + 3x2 = ((5 * -7 + 7x * -7) + x(5 + 7x))
35 + -26x + 3x2 = ((-35 + -49x) + x(5 + 7x))
35 + -26x + 3x2 = (-35 + -49x + (5 * x + 7x * x))
35 + -26x + 3x2 = (-35 + -49x + (5x + 7x2))

Combine like terms: -49x + 5x = -44x
35 + -26x + 3x2 = (-35 + -44x + 7x2)

Solving
35 + -26x + 3x2 = -35 + -44x + 7x2

Solving for variable 'x'.

Reorder the terms:
35 + 35 + -26x + 44x + 3x2 + -7x2 = -35 + -44x + 7x2 + 35 + 44x + -7x2

Combine like terms: 35 + 35 = 70
70 + -26x + 44x + 3x2 + -7x2 = -35 + -44x + 7x2 + 35 + 44x + -7x2

Combine like terms: -26x + 44x = 18x
70 + 18x + 3x2 + -7x2 = -35 + -44x + 7x2 + 35 + 44x + -7x2

Combine like terms: 3x2 + -7x2 = -4x2
70 + 18x + -4x2 = -35 + -44x + 7x2 + 35 + 44x + -7x2

Reorder the terms:
70 + 18x + -4x2 = -35 + 35 + -44x + 44x + 7x2 + -7x2

Combine like terms: -35 + 35 = 0
70 + 18x + -4x2 = 0 + -44x + 44x + 7x2 + -7x2
70 + 18x + -4x2 = -44x + 44x + 7x2 + -7x2

Combine like terms: -44x + 44x = 0
70 + 18x + -4x2 = 0 + 7x2 + -7x2
70 + 18x + -4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
70 + 18x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + 9x + -2x2) = 0

Factor a trinomial.
2((7 + -1x)(5 + 2x)) = 0

Ignore the factor 2.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {7, -2.5}

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