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

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


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

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

Multiply (-3 + x) * (5 + 2x)
0 = (-3(5 + 2x) + x(5 + 2x))
0 = ((5 * -3 + 2x * -3) + x(5 + 2x))
0 = ((-15 + -6x) + x(5 + 2x))
0 = (-15 + -6x + (5 * x + 2x * x))
0 = (-15 + -6x + (5x + 2x2))

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

Solving
0 = -15 + -1x + 2x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2x2 + -2x2 = 0
15 + x + -2x2 = 0

Factor a trinomial.
(3 + -1x)(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {3, -2.5}

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