(x+5)(x-2)+3(x+1)=0

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Solution for (x+5)(x-2)+3(x+1)=0 equation: 


Simplifying
(x + 5)(x + -2) + 3(x + 1) = 0

Reorder the terms:
(5 + x)(x + -2) + 3(x + 1) = 0

Reorder the terms:
(5 + x)(-2 + x) + 3(x + 1) = 0

Multiply (5 + x) * (-2 + x)
(5(-2 + x) + x(-2 + x)) + 3(x + 1) = 0
((-2 * 5 + x * 5) + x(-2 + x)) + 3(x + 1) = 0
((-10 + 5x) + x(-2 + x)) + 3(x + 1) = 0
(-10 + 5x + (-2 * x + x * x)) + 3(x + 1) = 0
(-10 + 5x + (-2x + x2)) + 3(x + 1) = 0

Combine like terms: 5x + -2x = 3x
(-10 + 3x + x2) + 3(x + 1) = 0

Reorder the terms:
-10 + 3x + x2 + 3(1 + x) = 0
-10 + 3x + x2 + (1 * 3 + x * 3) = 0
-10 + 3x + x2 + (3 + 3x) = 0

Reorder the terms:
-10 + 3 + 3x + 3x + x2 = 0

Combine like terms: -10 + 3 = -7
-7 + 3x + 3x + x2 = 0

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

Solving
-7 + 6x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 1}

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