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

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


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

Reorder the terms:
2(5 + 3x) + (x + 2)(x + -3) = 0
(5 * 2 + 3x * 2) + (x + 2)(x + -3) = 0
(10 + 6x) + (x + 2)(x + -3) = 0

Reorder the terms:
10 + 6x + (2 + x)(x + -3) = 0

Reorder the terms:
10 + 6x + (2 + x)(-3 + x) = 0

Multiply (2 + x) * (-3 + x)
10 + 6x + (2(-3 + x) + x(-3 + x)) = 0
10 + 6x + ((-3 * 2 + x * 2) + x(-3 + x)) = 0
10 + 6x + ((-6 + 2x) + x(-3 + x)) = 0
10 + 6x + (-6 + 2x + (-3 * x + x * x)) = 0
10 + 6x + (-6 + 2x + (-3x + x2)) = 0

Combine like terms: 2x + -3x = -1x
10 + 6x + (-6 + -1x + x2) = 0

Reorder the terms:
10 + -6 + 6x + -1x + x2 = 0

Combine like terms: 10 + -6 = 4
4 + 6x + -1x + x2 = 0

Combine like terms: 6x + -1x = 5x
4 + 5x + x2 = 0

Solving
4 + 5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(1 + x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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