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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
-15 + 1x + 2x2 = x(3 + x)
-15 + 1x + 2x2 = (3 * x + x * x)
-15 + 1x + 2x2 = (3x + x2)

Solving
-15 + 1x + 2x2 = 3x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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