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

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


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

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

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

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

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

Reorder the terms:
-3 + 5 + -1x + 2x2 = (2x + 1)(3x + -2)

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

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

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

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

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

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

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

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

Solving
2 + 2x2 = -2 + 6x2

Solving for variable 'x'.

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

Add '-6x2' to each side of the equation.
2 + 2x2 + -6x2 = -2 + 6x2 + -6x2

Combine like terms: 2x2 + -6x2 = -4x2
2 + -4x2 = -2 + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
2 + -4x2 = -2 + 0
2 + -4x2 = -2

Add '-2' to each side of the equation.
2 + -2 + -4x2 = -2 + -2

Combine like terms: 2 + -2 = 0
0 + -4x2 = -2 + -2
-4x2 = -2 + -2

Combine like terms: -2 + -2 = -4
-4x2 = -4

Divide each side by '-4'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}

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