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

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

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

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

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

Multiply (2 + x) * (-3 + 2x)
(2(-3 + 2x) + x(-3 + 2x)) = 2(x + 1)(x + 5)
((-3 * 2 + 2x * 2) + x(-3 + 2x)) = 2(x + 1)(x + 5)
((-6 + 4x) + x(-3 + 2x)) = 2(x + 1)(x + 5)
(-6 + 4x + (-3 * x + 2x * x)) = 2(x + 1)(x + 5)
(-6 + 4x + (-3x + 2x2)) = 2(x + 1)(x + 5)

Combine like terms: 4x + -3x = 1x
(-6 + 1x + 2x2) = 2(x + 1)(x + 5)

Reorder the terms:
-6 + 1x + 2x2 = 2(1 + x)(x + 5)

Reorder the terms:
-6 + 1x + 2x2 = 2(1 + x)(5 + x)

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

Combine like terms: 1x + 5x = 6x
-6 + 1x + 2x2 = 2(5 + 6x + x2)
-6 + 1x + 2x2 = (5 * 2 + 6x * 2 + x2 * 2)
-6 + 1x + 2x2 = (10 + 12x + 2x2)

Add '-2x2' to each side of the equation.
-6 + 1x + 2x2 + -2x2 = 10 + 12x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 1x + 0 = 10 + 12x + 2x2 + -2x2
-6 + 1x = 10 + 12x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 1x = 10 + 12x + 0
-6 + 1x = 10 + 12x

Solving
-6 + 1x = 10 + 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
-6 + 1x + -12x = 10 + 12x + -12x

Combine like terms: 1x + -12x = -11x
-6 + -11x = 10 + 12x + -12x

Combine like terms: 12x + -12x = 0
-6 + -11x = 10 + 0
-6 + -11x = 10

Add '6' to each side of the equation.
-6 + 6 + -11x = 10 + 6

Combine like terms: -6 + 6 = 0
0 + -11x = 10 + 6
-11x = 10 + 6

Combine like terms: 10 + 6 = 16
-11x = 16

Divide each side by '-11'.
x = -1.454545455

Simplifying
x = -1.454545455