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

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

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

Reorder the terms for easier multiplication:
2 * 5x = (2x + 3)(x + 1)

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

Reorder the terms:
10x = (3 + 2x)(x + 1)

Reorder the terms:
10x = (3 + 2x)(1 + x)

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

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

Solving
10x = 3 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + 10x + -5x + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2

Combine like terms: 10x + -5x = 5x
-3 + 5x + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2

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

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

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

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

Factor a trinomial.
(-3 + 2x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
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 = {1.5, 1}