(x-7)(1-3x)=(7x-8)(1-3x)

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Solution for (x-7)(1-3x)=(7x-8)(1-3x) equation: 


Simplifying
(x + -7)(1 + -3x) = (7x + -8)(1 + -3x)

Reorder the terms:
(-7 + x)(1 + -3x) = (7x + -8)(1 + -3x)

Multiply (-7 + x) * (1 + -3x)
(-7(1 + -3x) + x(1 + -3x)) = (7x + -8)(1 + -3x)
((1 * -7 + -3x * -7) + x(1 + -3x)) = (7x + -8)(1 + -3x)
((-7 + 21x) + x(1 + -3x)) = (7x + -8)(1 + -3x)
(-7 + 21x + (1 * x + -3x * x)) = (7x + -8)(1 + -3x)
(-7 + 21x + (1x + -3x2)) = (7x + -8)(1 + -3x)

Combine like terms: 21x + 1x = 22x
(-7 + 22x + -3x2) = (7x + -8)(1 + -3x)

Reorder the terms:
-7 + 22x + -3x2 = (-8 + 7x)(1 + -3x)

Multiply (-8 + 7x) * (1 + -3x)
-7 + 22x + -3x2 = (-8(1 + -3x) + 7x * (1 + -3x))
-7 + 22x + -3x2 = ((1 * -8 + -3x * -8) + 7x * (1 + -3x))
-7 + 22x + -3x2 = ((-8 + 24x) + 7x * (1 + -3x))
-7 + 22x + -3x2 = (-8 + 24x + (1 * 7x + -3x * 7x))
-7 + 22x + -3x2 = (-8 + 24x + (7x + -21x2))

Combine like terms: 24x + 7x = 31x
-7 + 22x + -3x2 = (-8 + 31x + -21x2)

Solving
-7 + 22x + -3x2 = -8 + 31x + -21x2

Solving for variable 'x'.

Reorder the terms:
-7 + 8 + 22x + -31x + -3x2 + 21x2 = -8 + 31x + -21x2 + 8 + -31x + 21x2

Combine like terms: -7 + 8 = 1
1 + 22x + -31x + -3x2 + 21x2 = -8 + 31x + -21x2 + 8 + -31x + 21x2

Combine like terms: 22x + -31x = -9x
1 + -9x + -3x2 + 21x2 = -8 + 31x + -21x2 + 8 + -31x + 21x2

Combine like terms: -3x2 + 21x2 = 18x2
1 + -9x + 18x2 = -8 + 31x + -21x2 + 8 + -31x + 21x2

Reorder the terms:
1 + -9x + 18x2 = -8 + 8 + 31x + -31x + -21x2 + 21x2

Combine like terms: -8 + 8 = 0
1 + -9x + 18x2 = 0 + 31x + -31x + -21x2 + 21x2
1 + -9x + 18x2 = 31x + -31x + -21x2 + 21x2

Combine like terms: 31x + -31x = 0
1 + -9x + 18x2 = 0 + -21x2 + 21x2
1 + -9x + 18x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
1 + -9x + 18x2 = 0

Factor a trinomial.
(1 + -6x)(1 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0.1666666667, 0.3333333333}

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