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

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


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

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

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

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

Combine like terms: -3x + 2x = -1x
(-2 + -1x + 3x2) = -7(x + -1)

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

Solving
-2 + -1x + 3x2 = 7 + -7x

Solving for variable 'x'.

Reorder the terms:
-2 + -7 + -1x + 7x + 3x2 = 7 + -7x + -7 + 7x

Combine like terms: -2 + -7 = -9
-9 + -1x + 7x + 3x2 = 7 + -7x + -7 + 7x

Combine like terms: -1x + 7x = 6x
-9 + 6x + 3x2 = 7 + -7x + -7 + 7x

Reorder the terms:
-9 + 6x + 3x2 = 7 + -7 + -7x + 7x

Combine like terms: 7 + -7 = 0
-9 + 6x + 3x2 = 0 + -7x + 7x
-9 + 6x + 3x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-9 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 1}

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