(x-7)(3x-5)=(9x-4)(x-7)

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Solution for (x-7)(3x-5)=(9x-4)(x-7) equation:


Simplifying
(x + -7)(3x + -5) = (9x + -4)(x + -7)

Reorder the terms:
(-7 + x)(3x + -5) = (9x + -4)(x + -7)

Reorder the terms:
(-7 + x)(-5 + 3x) = (9x + -4)(x + -7)

Multiply (-7 + x) * (-5 + 3x)
(-7(-5 + 3x) + x(-5 + 3x)) = (9x + -4)(x + -7)
((-5 * -7 + 3x * -7) + x(-5 + 3x)) = (9x + -4)(x + -7)
((35 + -21x) + x(-5 + 3x)) = (9x + -4)(x + -7)
(35 + -21x + (-5 * x + 3x * x)) = (9x + -4)(x + -7)
(35 + -21x + (-5x + 3x2)) = (9x + -4)(x + -7)

Combine like terms: -21x + -5x = -26x
(35 + -26x + 3x2) = (9x + -4)(x + -7)

Reorder the terms:
35 + -26x + 3x2 = (-4 + 9x)(x + -7)

Reorder the terms:
35 + -26x + 3x2 = (-4 + 9x)(-7 + x)

Multiply (-4 + 9x) * (-7 + x)
35 + -26x + 3x2 = (-4(-7 + x) + 9x * (-7 + x))
35 + -26x + 3x2 = ((-7 * -4 + x * -4) + 9x * (-7 + x))
35 + -26x + 3x2 = ((28 + -4x) + 9x * (-7 + x))
35 + -26x + 3x2 = (28 + -4x + (-7 * 9x + x * 9x))
35 + -26x + 3x2 = (28 + -4x + (-63x + 9x2))

Combine like terms: -4x + -63x = -67x
35 + -26x + 3x2 = (28 + -67x + 9x2)

Solving
35 + -26x + 3x2 = 28 + -67x + 9x2

Solving for variable 'x'.

Reorder the terms:
35 + -28 + -26x + 67x + 3x2 + -9x2 = 28 + -67x + 9x2 + -28 + 67x + -9x2

Combine like terms: 35 + -28 = 7
7 + -26x + 67x + 3x2 + -9x2 = 28 + -67x + 9x2 + -28 + 67x + -9x2

Combine like terms: -26x + 67x = 41x
7 + 41x + 3x2 + -9x2 = 28 + -67x + 9x2 + -28 + 67x + -9x2

Combine like terms: 3x2 + -9x2 = -6x2
7 + 41x + -6x2 = 28 + -67x + 9x2 + -28 + 67x + -9x2

Reorder the terms:
7 + 41x + -6x2 = 28 + -28 + -67x + 67x + 9x2 + -9x2

Combine like terms: 28 + -28 = 0
7 + 41x + -6x2 = 0 + -67x + 67x + 9x2 + -9x2
7 + 41x + -6x2 = -67x + 67x + 9x2 + -9x2

Combine like terms: -67x + 67x = 0
7 + 41x + -6x2 = 0 + 9x2 + -9x2
7 + 41x + -6x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
7 + 41x + -6x2 = 0

Factor a trinomial.
(7 + -1x)(1 + 6x) = 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 '(1 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {7, -0.1666666667}

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