(7x-6)(x-5)=(x+3)(1-2x)

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Solution for (7x-6)(x-5)=(x+3)(1-2x) equation: 


Simplifying
(7x + -6)(x + -5) = (x + 3)(1 + -2x)

Reorder the terms:
(-6 + 7x)(x + -5) = (x + 3)(1 + -2x)

Reorder the terms:
(-6 + 7x)(-5 + x) = (x + 3)(1 + -2x)

Multiply (-6 + 7x) * (-5 + x)
(-6(-5 + x) + 7x * (-5 + x)) = (x + 3)(1 + -2x)
((-5 * -6 + x * -6) + 7x * (-5 + x)) = (x + 3)(1 + -2x)
((30 + -6x) + 7x * (-5 + x)) = (x + 3)(1 + -2x)
(30 + -6x + (-5 * 7x + x * 7x)) = (x + 3)(1 + -2x)
(30 + -6x + (-35x + 7x2)) = (x + 3)(1 + -2x)

Combine like terms: -6x + -35x = -41x
(30 + -41x + 7x2) = (x + 3)(1 + -2x)

Reorder the terms:
30 + -41x + 7x2 = (3 + x)(1 + -2x)

Multiply (3 + x) * (1 + -2x)
30 + -41x + 7x2 = (3(1 + -2x) + x(1 + -2x))
30 + -41x + 7x2 = ((1 * 3 + -2x * 3) + x(1 + -2x))
30 + -41x + 7x2 = ((3 + -6x) + x(1 + -2x))
30 + -41x + 7x2 = (3 + -6x + (1 * x + -2x * x))
30 + -41x + 7x2 = (3 + -6x + (1x + -2x2))

Combine like terms: -6x + 1x = -5x
30 + -41x + 7x2 = (3 + -5x + -2x2)

Solving
30 + -41x + 7x2 = 3 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
30 + -3 + -41x + 5x + 7x2 + 2x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2

Combine like terms: 30 + -3 = 27
27 + -41x + 5x + 7x2 + 2x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2

Combine like terms: -41x + 5x = -36x
27 + -36x + 7x2 + 2x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2

Combine like terms: 7x2 + 2x2 = 9x2
27 + -36x + 9x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2

Reorder the terms:
27 + -36x + 9x2 = 3 + -3 + -5x + 5x + -2x2 + 2x2

Combine like terms: 3 + -3 = 0
27 + -36x + 9x2 = 0 + -5x + 5x + -2x2 + 2x2
27 + -36x + 9x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
27 + -36x + 9x2 = 0 + -2x2 + 2x2
27 + -36x + 9x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
27 + -36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + -4x + x2) = 0

Factor a trinomial.
9((1 + -1x)(3 + -1x)) = 0

Ignore the factor 9.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}

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