2x(x-5)-(2x-3)(x+1)=x(2-x)-15

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Solution for 2x(x-5)-(2x-3)(x+1)=x(2-x)-15 equation:


Simplifying
2x(x + -5) + -1(2x + -3)(x + 1) = x(2 + -1x) + -15

Reorder the terms:
2x(-5 + x) + -1(2x + -3)(x + 1) = x(2 + -1x) + -15
(-5 * 2x + x * 2x) + -1(2x + -3)(x + 1) = x(2 + -1x) + -15
(-10x + 2x2) + -1(2x + -3)(x + 1) = x(2 + -1x) + -15

Reorder the terms:
-10x + 2x2 + -1(-3 + 2x)(x + 1) = x(2 + -1x) + -15

Reorder the terms:
-10x + 2x2 + -1(-3 + 2x)(1 + x) = x(2 + -1x) + -15

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

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

Reorder the terms:
3 + -10x + 1x + 2x2 + -2x2 = x(2 + -1x) + -15

Combine like terms: -10x + 1x = -9x
3 + -9x + 2x2 + -2x2 = x(2 + -1x) + -15

Combine like terms: 2x2 + -2x2 = 0
3 + -9x + 0 = x(2 + -1x) + -15
3 + -9x = x(2 + -1x) + -15
3 + -9x = (2 * x + -1x * x) + -15
3 + -9x = (2x + -1x2) + -15

Reorder the terms:
3 + -9x = -15 + 2x + -1x2

Solving
3 + -9x = -15 + 2x + -1x2

Solving for variable 'x'.

Reorder the terms:
3 + 15 + -9x + -2x + x2 = -15 + 2x + -1x2 + 15 + -2x + x2

Combine like terms: 3 + 15 = 18
18 + -9x + -2x + x2 = -15 + 2x + -1x2 + 15 + -2x + x2

Combine like terms: -9x + -2x = -11x
18 + -11x + x2 = -15 + 2x + -1x2 + 15 + -2x + x2

Reorder the terms:
18 + -11x + x2 = -15 + 15 + 2x + -2x + -1x2 + x2

Combine like terms: -15 + 15 = 0
18 + -11x + x2 = 0 + 2x + -2x + -1x2 + x2
18 + -11x + x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
18 + -11x + x2 = 0 + -1x2 + x2
18 + -11x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
18 + -11x + x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {2, 9}

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