2x(x-5)-(x-3)(x+2)=28-3(3x-1)(3x+2)

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Solution for 2x(x-5)-(x-3)(x+2)=28-3(3x-1)(3x+2) equation:


Simplifying
2x(x + -5) + -1(x + -3)(x + 2) = 28 + -3(3x + -1)(3x + 2)

Reorder the terms:
2x(-5 + x) + -1(x + -3)(x + 2) = 28 + -3(3x + -1)(3x + 2)
(-5 * 2x + x * 2x) + -1(x + -3)(x + 2) = 28 + -3(3x + -1)(3x + 2)
(-10x + 2x2) + -1(x + -3)(x + 2) = 28 + -3(3x + -1)(3x + 2)

Reorder the terms:
-10x + 2x2 + -1(-3 + x)(x + 2) = 28 + -3(3x + -1)(3x + 2)

Reorder the terms:
-10x + 2x2 + -1(-3 + x)(2 + x) = 28 + -3(3x + -1)(3x + 2)

Multiply (-3 + x) * (2 + x)
-10x + 2x2 + -1(-3(2 + x) + x(2 + x)) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + -1((2 * -3 + x * -3) + x(2 + x)) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + -1((-6 + -3x) + x(2 + x)) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + -1(-6 + -3x + (2 * x + x * x)) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + -1(-6 + -3x + (2x + x2)) = 28 + -3(3x + -1)(3x + 2)

Combine like terms: -3x + 2x = -1x
-10x + 2x2 + -1(-6 + -1x + x2) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + (-6 * -1 + -1x * -1 + x2 * -1) = 28 + -3(3x + -1)(3x + 2)
-10x + 2x2 + (6 + 1x + -1x2) = 28 + -3(3x + -1)(3x + 2)

Reorder the terms:
6 + -10x + 1x + 2x2 + -1x2 = 28 + -3(3x + -1)(3x + 2)

Combine like terms: -10x + 1x = -9x
6 + -9x + 2x2 + -1x2 = 28 + -3(3x + -1)(3x + 2)

Combine like terms: 2x2 + -1x2 = 1x2
6 + -9x + 1x2 = 28 + -3(3x + -1)(3x + 2)

Reorder the terms:
6 + -9x + 1x2 = 28 + -3(-1 + 3x)(3x + 2)

Reorder the terms:
6 + -9x + 1x2 = 28 + -3(-1 + 3x)(2 + 3x)

Multiply (-1 + 3x) * (2 + 3x)
6 + -9x + 1x2 = 28 + -3(-1(2 + 3x) + 3x * (2 + 3x))
6 + -9x + 1x2 = 28 + -3((2 * -1 + 3x * -1) + 3x * (2 + 3x))
6 + -9x + 1x2 = 28 + -3((-2 + -3x) + 3x * (2 + 3x))
6 + -9x + 1x2 = 28 + -3(-2 + -3x + (2 * 3x + 3x * 3x))
6 + -9x + 1x2 = 28 + -3(-2 + -3x + (6x + 9x2))

Combine like terms: -3x + 6x = 3x
6 + -9x + 1x2 = 28 + -3(-2 + 3x + 9x2)
6 + -9x + 1x2 = 28 + (-2 * -3 + 3x * -3 + 9x2 * -3)
6 + -9x + 1x2 = 28 + (6 + -9x + -27x2)

Combine like terms: 28 + 6 = 34
6 + -9x + 1x2 = 34 + -9x + -27x2

Add '9x' to each side of the equation.
6 + -9x + 9x + 1x2 = 34 + -9x + 9x + -27x2

Combine like terms: -9x + 9x = 0
6 + 0 + 1x2 = 34 + -9x + 9x + -27x2
6 + 1x2 = 34 + -9x + 9x + -27x2

Combine like terms: -9x + 9x = 0
6 + 1x2 = 34 + 0 + -27x2
6 + 1x2 = 34 + -27x2

Solving
6 + 1x2 = 34 + -27x2

Solving for variable 'x'.

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

Add '27x2' to each side of the equation.
6 + 1x2 + 27x2 = 34 + -27x2 + 27x2

Combine like terms: 1x2 + 27x2 = 28x2
6 + 28x2 = 34 + -27x2 + 27x2

Combine like terms: -27x2 + 27x2 = 0
6 + 28x2 = 34 + 0
6 + 28x2 = 34

Add '-6' to each side of the equation.
6 + -6 + 28x2 = 34 + -6

Combine like terms: 6 + -6 = 0
0 + 28x2 = 34 + -6
28x2 = 34 + -6

Combine like terms: 34 + -6 = 28
28x2 = 28

Divide each side by '28'.
x2 = 1

Simplifying
x2 = 1

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

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