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

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

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

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

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

Multiply (3 + x) * (-5 + 2x)
(3(-5 + 2x) + x(-5 + 2x)) = 2(x + 1)(x + 3)
((-5 * 3 + 2x * 3) + x(-5 + 2x)) = 2(x + 1)(x + 3)
((-15 + 6x) + x(-5 + 2x)) = 2(x + 1)(x + 3)
(-15 + 6x + (-5 * x + 2x * x)) = 2(x + 1)(x + 3)
(-15 + 6x + (-5x + 2x2)) = 2(x + 1)(x + 3)

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

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

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

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

Combine like terms: 1x + 3x = 4x
-15 + 1x + 2x2 = 2(3 + 4x + x2)
-15 + 1x + 2x2 = (3 * 2 + 4x * 2 + x2 * 2)
-15 + 1x + 2x2 = (6 + 8x + 2x2)

Add '-2x2' to each side of the equation.
-15 + 1x + 2x2 + -2x2 = 6 + 8x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 1x + 0 = 6 + 8x + 2x2 + -2x2
-15 + 1x = 6 + 8x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 1x = 6 + 8x + 0
-15 + 1x = 6 + 8x

Solving
-15 + 1x = 6 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
-15 + 1x + -8x = 6 + 8x + -8x

Combine like terms: 1x + -8x = -7x
-15 + -7x = 6 + 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + -7x = 6 + 0
-15 + -7x = 6

Add '15' to each side of the equation.
-15 + 15 + -7x = 6 + 15

Combine like terms: -15 + 15 = 0
0 + -7x = 6 + 15
-7x = 6 + 15

Combine like terms: 6 + 15 = 21
-7x = 21

Divide each side by '-7'.
x = -3

Simplifying
x = -3