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

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


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

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

Multiply (3 + x) * (5 + -1x)
(3(5 + -1x) + x(5 + -1x)) + (x + 3)(2x + -1) = 0
((5 * 3 + -1x * 3) + x(5 + -1x)) + (x + 3)(2x + -1) = 0
((15 + -3x) + x(5 + -1x)) + (x + 3)(2x + -1) = 0
(15 + -3x + (5 * x + -1x * x)) + (x + 3)(2x + -1) = 0
(15 + -3x + (5x + -1x2)) + (x + 3)(2x + -1) = 0

Combine like terms: -3x + 5x = 2x
(15 + 2x + -1x2) + (x + 3)(2x + -1) = 0

Reorder the terms:
15 + 2x + -1x2 + (3 + x)(2x + -1) = 0

Reorder the terms:
15 + 2x + -1x2 + (3 + x)(-1 + 2x) = 0

Multiply (3 + x) * (-1 + 2x)
15 + 2x + -1x2 + (3(-1 + 2x) + x(-1 + 2x)) = 0
15 + 2x + -1x2 + ((-1 * 3 + 2x * 3) + x(-1 + 2x)) = 0
15 + 2x + -1x2 + ((-3 + 6x) + x(-1 + 2x)) = 0
15 + 2x + -1x2 + (-3 + 6x + (-1 * x + 2x * x)) = 0
15 + 2x + -1x2 + (-3 + 6x + (-1x + 2x2)) = 0

Combine like terms: 6x + -1x = 5x
15 + 2x + -1x2 + (-3 + 5x + 2x2) = 0

Reorder the terms:
15 + -3 + 2x + 5x + -1x2 + 2x2 = 0

Combine like terms: 15 + -3 = 12
12 + 2x + 5x + -1x2 + 2x2 = 0

Combine like terms: 2x + 5x = 7x
12 + 7x + -1x2 + 2x2 = 0

Combine like terms: -1x2 + 2x2 = 1x2
12 + 7x + 1x2 = 0

Solving
12 + 7x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}

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