(5x+1)*(2x-3)-(3x+1)*(3x-2)-x*(x+1)=0

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Solution for (5x+1)*(2x-3)-(3x+1)*(3x-2)-x*(x+1)=0 equation: 


Simplifying
(5x + 1)(2x + -3) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0

Reorder the terms:
(1 + 5x)(2x + -3) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0

Reorder the terms:
(1 + 5x)(-3 + 2x) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0

Multiply (1 + 5x) * (-3 + 2x)
(1(-3 + 2x) + 5x * (-3 + 2x)) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0
((-3 * 1 + 2x * 1) + 5x * (-3 + 2x)) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0
((-3 + 2x) + 5x * (-3 + 2x)) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0
(-3 + 2x + (-3 * 5x + 2x * 5x)) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0
(-3 + 2x + (-15x + 10x2)) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0

Combine like terms: 2x + -15x = -13x
(-3 + -13x + 10x2) + -1(3x + 1)(3x + -2) + -1x(x + 1) = 0

Reorder the terms:
-3 + -13x + 10x2 + -1(1 + 3x)(3x + -2) + -1x(x + 1) = 0

Reorder the terms:
-3 + -13x + 10x2 + -1(1 + 3x)(-2 + 3x) + -1x(x + 1) = 0

Multiply (1 + 3x) * (-2 + 3x)
-3 + -13x + 10x2 + -1(1(-2 + 3x) + 3x * (-2 + 3x)) + -1x(x + 1) = 0
-3 + -13x + 10x2 + -1((-2 * 1 + 3x * 1) + 3x * (-2 + 3x)) + -1x(x + 1) = 0
-3 + -13x + 10x2 + -1((-2 + 3x) + 3x * (-2 + 3x)) + -1x(x + 1) = 0
-3 + -13x + 10x2 + -1(-2 + 3x + (-2 * 3x + 3x * 3x)) + -1x(x + 1) = 0
-3 + -13x + 10x2 + -1(-2 + 3x + (-6x + 9x2)) + -1x(x + 1) = 0

Combine like terms: 3x + -6x = -3x
-3 + -13x + 10x2 + -1(-2 + -3x + 9x2) + -1x(x + 1) = 0
-3 + -13x + 10x2 + (-2 * -1 + -3x * -1 + 9x2 * -1) + -1x(x + 1) = 0
-3 + -13x + 10x2 + (2 + 3x + -9x2) + -1x(x + 1) = 0

Reorder the terms:
-3 + -13x + 10x2 + 2 + 3x + -9x2 + -1x(1 + x) = 0
-3 + -13x + 10x2 + 2 + 3x + -9x2 + (1 * -1x + x * -1x) = 0
-3 + -13x + 10x2 + 2 + 3x + -9x2 + (-1x + -1x2) = 0

Reorder the terms:
-3 + 2 + -13x + 3x + -1x + 10x2 + -9x2 + -1x2 = 0

Combine like terms: -3 + 2 = -1
-1 + -13x + 3x + -1x + 10x2 + -9x2 + -1x2 = 0

Combine like terms: -13x + 3x = -10x
-1 + -10x + -1x + 10x2 + -9x2 + -1x2 = 0

Combine like terms: -10x + -1x = -11x
-1 + -11x + 10x2 + -9x2 + -1x2 = 0

Combine like terms: 10x2 + -9x2 = 1x2
-1 + -11x + 1x2 + -1x2 = 0

Combine like terms: 1x2 + -1x2 = 0
-1 + -11x + 0 = 0
-1 + -11x = 0

Solving
-1 + -11x = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + -11x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -11x = 0 + 1
-11x = 0 + 1

Combine like terms: 0 + 1 = 1
-11x = 1

Divide each side by '-11'.
x = -0.09090909091

Simplifying
x = -0.09090909091

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