(x-1)(5x+2)=-13(x-1)

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Solution for (x-1)(5x+2)=-13(x-1) equation: 


Simplifying
(x + -1)(5x + 2) = -13(x + -1)

Reorder the terms:
(-1 + x)(5x + 2) = -13(x + -1)

Reorder the terms:
(-1 + x)(2 + 5x) = -13(x + -1)

Multiply (-1 + x) * (2 + 5x)
(-1(2 + 5x) + x(2 + 5x)) = -13(x + -1)
((2 * -1 + 5x * -1) + x(2 + 5x)) = -13(x + -1)
((-2 + -5x) + x(2 + 5x)) = -13(x + -1)
(-2 + -5x + (2 * x + 5x * x)) = -13(x + -1)
(-2 + -5x + (2x + 5x2)) = -13(x + -1)

Combine like terms: -5x + 2x = -3x
(-2 + -3x + 5x2) = -13(x + -1)

Reorder the terms:
-2 + -3x + 5x2 = -13(-1 + x)
-2 + -3x + 5x2 = (-1 * -13 + x * -13)
-2 + -3x + 5x2 = (13 + -13x)

Solving
-2 + -3x + 5x2 = 13 + -13x

Solving for variable 'x'.

Reorder the terms:
-2 + -13 + -3x + 13x + 5x2 = 13 + -13x + -13 + 13x

Combine like terms: -2 + -13 = -15
-15 + -3x + 13x + 5x2 = 13 + -13x + -13 + 13x

Combine like terms: -3x + 13x = 10x
-15 + 10x + 5x2 = 13 + -13x + -13 + 13x

Reorder the terms:
-15 + 10x + 5x2 = 13 + -13 + -13x + 13x

Combine like terms: 13 + -13 = 0
-15 + 10x + 5x2 = 0 + -13x + 13x
-15 + 10x + 5x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-15 + 10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 2x + x2) = 0

Factor a trinomial.
5((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 5.

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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