(x-5)(-x+4)-(x-1)(x+3)=-2x^2

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Solution for (x-5)(-x+4)-(x-1)(x+3)=-2x^2 equation: 


Simplifying
(x + -5)(-1x + 4) + -1(x + -1)(x + 3) = -2x2

Reorder the terms:
(-5 + x)(-1x + 4) + -1(x + -1)(x + 3) = -2x2

Reorder the terms:
(-5 + x)(4 + -1x) + -1(x + -1)(x + 3) = -2x2

Multiply (-5 + x) * (4 + -1x)
(-5(4 + -1x) + x(4 + -1x)) + -1(x + -1)(x + 3) = -2x2
((4 * -5 + -1x * -5) + x(4 + -1x)) + -1(x + -1)(x + 3) = -2x2
((-20 + 5x) + x(4 + -1x)) + -1(x + -1)(x + 3) = -2x2
(-20 + 5x + (4 * x + -1x * x)) + -1(x + -1)(x + 3) = -2x2
(-20 + 5x + (4x + -1x2)) + -1(x + -1)(x + 3) = -2x2

Combine like terms: 5x + 4x = 9x
(-20 + 9x + -1x2) + -1(x + -1)(x + 3) = -2x2

Reorder the terms:
-20 + 9x + -1x2 + -1(-1 + x)(x + 3) = -2x2

Reorder the terms:
-20 + 9x + -1x2 + -1(-1 + x)(3 + x) = -2x2

Multiply (-1 + x) * (3 + x)
-20 + 9x + -1x2 + -1(-1(3 + x) + x(3 + x)) = -2x2
-20 + 9x + -1x2 + -1((3 * -1 + x * -1) + x(3 + x)) = -2x2
-20 + 9x + -1x2 + -1((-3 + -1x) + x(3 + x)) = -2x2
-20 + 9x + -1x2 + -1(-3 + -1x + (3 * x + x * x)) = -2x2
-20 + 9x + -1x2 + -1(-3 + -1x + (3x + x2)) = -2x2

Combine like terms: -1x + 3x = 2x
-20 + 9x + -1x2 + -1(-3 + 2x + x2) = -2x2
-20 + 9x + -1x2 + (-3 * -1 + 2x * -1 + x2 * -1) = -2x2
-20 + 9x + -1x2 + (3 + -2x + -1x2) = -2x2

Reorder the terms:
-20 + 3 + 9x + -2x + -1x2 + -1x2 = -2x2

Combine like terms: -20 + 3 = -17
-17 + 9x + -2x + -1x2 + -1x2 = -2x2

Combine like terms: 9x + -2x = 7x
-17 + 7x + -1x2 + -1x2 = -2x2

Combine like terms: -1x2 + -1x2 = -2x2
-17 + 7x + -2x2 = -2x2

Add '2x2' to each side of the equation.
-17 + 7x + -2x2 + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-17 + 7x + 0 = -2x2 + 2x2
-17 + 7x = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-17 + 7x = 0

Solving
-17 + 7x = 0

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + 7x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 7x = 0 + 17
7x = 0 + 17

Combine like terms: 0 + 17 = 17
7x = 17

Divide each side by '7'.
x = 2.428571429

Simplifying
x = 2.428571429

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