(7x-6)(x-7)=(1-3x)(x+2)

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Solution for (7x-6)(x-7)=(1-3x)(x+2) equation: 


Simplifying
(7x + -6)(x + -7) = (1 + -3x)(x + 2)

Reorder the terms:
(-6 + 7x)(x + -7) = (1 + -3x)(x + 2)

Reorder the terms:
(-6 + 7x)(-7 + x) = (1 + -3x)(x + 2)

Multiply (-6 + 7x) * (-7 + x)
(-6(-7 + x) + 7x * (-7 + x)) = (1 + -3x)(x + 2)
((-7 * -6 + x * -6) + 7x * (-7 + x)) = (1 + -3x)(x + 2)
((42 + -6x) + 7x * (-7 + x)) = (1 + -3x)(x + 2)
(42 + -6x + (-7 * 7x + x * 7x)) = (1 + -3x)(x + 2)
(42 + -6x + (-49x + 7x2)) = (1 + -3x)(x + 2)

Combine like terms: -6x + -49x = -55x
(42 + -55x + 7x2) = (1 + -3x)(x + 2)

Reorder the terms:
42 + -55x + 7x2 = (1 + -3x)(2 + x)

Multiply (1 + -3x) * (2 + x)
42 + -55x + 7x2 = (1(2 + x) + -3x * (2 + x))
42 + -55x + 7x2 = ((2 * 1 + x * 1) + -3x * (2 + x))
42 + -55x + 7x2 = ((2 + 1x) + -3x * (2 + x))
42 + -55x + 7x2 = (2 + 1x + (2 * -3x + x * -3x))
42 + -55x + 7x2 = (2 + 1x + (-6x + -3x2))

Combine like terms: 1x + -6x = -5x
42 + -55x + 7x2 = (2 + -5x + -3x2)

Solving
42 + -55x + 7x2 = 2 + -5x + -3x2

Solving for variable 'x'.

Reorder the terms:
42 + -2 + -55x + 5x + 7x2 + 3x2 = 2 + -5x + -3x2 + -2 + 5x + 3x2

Combine like terms: 42 + -2 = 40
40 + -55x + 5x + 7x2 + 3x2 = 2 + -5x + -3x2 + -2 + 5x + 3x2

Combine like terms: -55x + 5x = -50x
40 + -50x + 7x2 + 3x2 = 2 + -5x + -3x2 + -2 + 5x + 3x2

Combine like terms: 7x2 + 3x2 = 10x2
40 + -50x + 10x2 = 2 + -5x + -3x2 + -2 + 5x + 3x2

Reorder the terms:
40 + -50x + 10x2 = 2 + -2 + -5x + 5x + -3x2 + 3x2

Combine like terms: 2 + -2 = 0
40 + -50x + 10x2 = 0 + -5x + 5x + -3x2 + 3x2
40 + -50x + 10x2 = -5x + 5x + -3x2 + 3x2

Combine like terms: -5x + 5x = 0
40 + -50x + 10x2 = 0 + -3x2 + 3x2
40 + -50x + 10x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
40 + -50x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(4 + -5x + x2) = 0

Factor a trinomial.
10((1 + -1x)(4 + -1x)) = 0

Ignore the factor 10.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}

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