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

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

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

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

Reorder the terms for easier multiplication:
2(-1 + 3x) + -1(2x + 3) * 2 = 5(x + -2) + (x + -1)(5x + 2)
(-1 * 2 + 3x * 2) + -1(2x + 3) * 2 = 5(x + -2) + (x + -1)(5x + 2)
(-2 + 6x) + -1(2x + 3) * 2 = 5(x + -2) + (x + -1)(5x + 2)

Reorder the terms:
-2 + 6x + -1(3 + 2x) * 2 = 5(x + -2) + (x + -1)(5x + 2)

Reorder the terms for easier multiplication:
-2 + 6x + -1 * 2(3 + 2x) = 5(x + -2) + (x + -1)(5x + 2)

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

Reorder the terms:
-2 + -6 + 6x + -4x = 5(x + -2) + (x + -1)(5x + 2)

Combine like terms: -2 + -6 = -8
-8 + 6x + -4x = 5(x + -2) + (x + -1)(5x + 2)

Combine like terms: 6x + -4x = 2x
-8 + 2x = 5(x + -2) + (x + -1)(5x + 2)

Reorder the terms:
-8 + 2x = 5(-2 + x) + (x + -1)(5x + 2)
-8 + 2x = (-2 * 5 + x * 5) + (x + -1)(5x + 2)
-8 + 2x = (-10 + 5x) + (x + -1)(5x + 2)

Reorder the terms:
-8 + 2x = -10 + 5x + (-1 + x)(5x + 2)

Reorder the terms:
-8 + 2x = -10 + 5x + (-1 + x)(2 + 5x)

Multiply (-1 + x) * (2 + 5x)
-8 + 2x = -10 + 5x + (-1(2 + 5x) + x(2 + 5x))
-8 + 2x = -10 + 5x + ((2 * -1 + 5x * -1) + x(2 + 5x))
-8 + 2x = -10 + 5x + ((-2 + -5x) + x(2 + 5x))
-8 + 2x = -10 + 5x + (-2 + -5x + (2 * x + 5x * x))
-8 + 2x = -10 + 5x + (-2 + -5x + (2x + 5x2))

Combine like terms: -5x + 2x = -3x
-8 + 2x = -10 + 5x + (-2 + -3x + 5x2)

Reorder the terms:
-8 + 2x = -10 + -2 + 5x + -3x + 5x2

Combine like terms: -10 + -2 = -12
-8 + 2x = -12 + 5x + -3x + 5x2

Combine like terms: 5x + -3x = 2x
-8 + 2x = -12 + 2x + 5x2

Add '-2x' to each side of the equation.
-8 + 2x + -2x = -12 + 2x + -2x + 5x2

Combine like terms: 2x + -2x = 0
-8 + 0 = -12 + 2x + -2x + 5x2
-8 = -12 + 2x + -2x + 5x2

Combine like terms: 2x + -2x = 0
-8 = -12 + 0 + 5x2
-8 = -12 + 5x2

Solving
-8 = -12 + 5x2

Solving for variable 'x'.

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

Add '-5x2' to each side of the equation.
-8 + -5x2 = -12 + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-8 + -5x2 = -12 + 0
-8 + -5x2 = -12

Add '8' to each side of the equation.
-8 + 8 + -5x2 = -12 + 8

Combine like terms: -8 + 8 = 0
0 + -5x2 = -12 + 8
-5x2 = -12 + 8

Combine like terms: -12 + 8 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}