(x-1)*(3x-2)=10x+20

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Solution for (x-1)*(3x-2)=10x+20 equation: 


Simplifying
(x + -1)(3x + -2) = 10x + 20

Reorder the terms:
(-1 + x)(3x + -2) = 10x + 20

Reorder the terms:
(-1 + x)(-2 + 3x) = 10x + 20

Multiply (-1 + x) * (-2 + 3x)
(-1(-2 + 3x) + x(-2 + 3x)) = 10x + 20
((-2 * -1 + 3x * -1) + x(-2 + 3x)) = 10x + 20
((2 + -3x) + x(-2 + 3x)) = 10x + 20
(2 + -3x + (-2 * x + 3x * x)) = 10x + 20
(2 + -3x + (-2x + 3x2)) = 10x + 20

Combine like terms: -3x + -2x = -5x
(2 + -5x + 3x2) = 10x + 20

Reorder the terms:
2 + -5x + 3x2 = 20 + 10x

Solving
2 + -5x + 3x2 = 20 + 10x

Solving for variable 'x'.

Reorder the terms:
2 + -20 + -5x + -10x + 3x2 = 20 + 10x + -20 + -10x

Combine like terms: 2 + -20 = -18
-18 + -5x + -10x + 3x2 = 20 + 10x + -20 + -10x

Combine like terms: -5x + -10x = -15x
-18 + -15x + 3x2 = 20 + 10x + -20 + -10x

Reorder the terms:
-18 + -15x + 3x2 = 20 + -20 + 10x + -10x

Combine like terms: 20 + -20 = 0
-18 + -15x + 3x2 = 0 + 10x + -10x
-18 + -15x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-18 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -5x + x2) = 0

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

Ignore the factor 3.

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}

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