(x-5)(x+2)=-4(x+1)

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Solution for (x-5)(x+2)=-4(x+1) equation: 


Simplifying
(x + -5)(x + 2) = -4(x + 1)

Reorder the terms:
(-5 + x)(x + 2) = -4(x + 1)

Reorder the terms:
(-5 + x)(2 + x) = -4(x + 1)

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x)) = -4(x + 1)
((2 * -5 + x * -5) + x(2 + x)) = -4(x + 1)
((-10 + -5x) + x(2 + x)) = -4(x + 1)
(-10 + -5x + (2 * x + x * x)) = -4(x + 1)
(-10 + -5x + (2x + x2)) = -4(x + 1)

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2) = -4(x + 1)

Reorder the terms:
-10 + -3x + x2 = -4(1 + x)
-10 + -3x + x2 = (1 * -4 + x * -4)
-10 + -3x + x2 = (-4 + -4x)

Solving
-10 + -3x + x2 = -4 + -4x

Solving for variable 'x'.

Reorder the terms:
-10 + 4 + -3x + 4x + x2 = -4 + -4x + 4 + 4x

Combine like terms: -10 + 4 = -6
-6 + -3x + 4x + x2 = -4 + -4x + 4 + 4x

Combine like terms: -3x + 4x = 1x
-6 + 1x + x2 = -4 + -4x + 4 + 4x

Reorder the terms:
-6 + 1x + x2 = -4 + 4 + -4x + 4x

Combine like terms: -4 + 4 = 0
-6 + 1x + x2 = 0 + -4x + 4x
-6 + 1x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-6 + 1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0


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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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