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

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


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

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

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

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

Combine like terms: -10x + 3x = -7x
(-15 + -7x + 2x2) + -2x(x + 1) = 0

Reorder the terms:
-15 + -7x + 2x2 + -2x(1 + x) = 0
-15 + -7x + 2x2 + (1 * -2x + x * -2x) = 0
-15 + -7x + 2x2 + (-2x + -2x2) = 0

Reorder the terms:
-15 + -7x + -2x + 2x2 + -2x2 = 0

Combine like terms: -7x + -2x = -9x
-15 + -9x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
-15 + -9x + 0 = 0
-15 + -9x = 0

Solving
-15 + -9x = 0

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + -9x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -9x = 0 + 15
-9x = 0 + 15

Combine like terms: 0 + 15 = 15
-9x = 15

Divide each side by '-9'.
x = -1.666666667

Simplifying
x = -1.666666667

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