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

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


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

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

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

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

Combine like terms: -1x + -2x = -3x
3(2 + -3x + x2) + -1(x + 3)(x + 5) = 0
(2 * 3 + -3x * 3 + x2 * 3) + -1(x + 3)(x + 5) = 0
(6 + -9x + 3x2) + -1(x + 3)(x + 5) = 0

Reorder the terms:
6 + -9x + 3x2 + -1(3 + x)(x + 5) = 0

Reorder the terms:
6 + -9x + 3x2 + -1(3 + x)(5 + x) = 0

Multiply (3 + x) * (5 + x)
6 + -9x + 3x2 + -1(3(5 + x) + x(5 + x)) = 0
6 + -9x + 3x2 + -1((5 * 3 + x * 3) + x(5 + x)) = 0
6 + -9x + 3x2 + -1((15 + 3x) + x(5 + x)) = 0
6 + -9x + 3x2 + -1(15 + 3x + (5 * x + x * x)) = 0
6 + -9x + 3x2 + -1(15 + 3x + (5x + x2)) = 0

Combine like terms: 3x + 5x = 8x
6 + -9x + 3x2 + -1(15 + 8x + x2) = 0
6 + -9x + 3x2 + (15 * -1 + 8x * -1 + x2 * -1) = 0
6 + -9x + 3x2 + (-15 + -8x + -1x2) = 0

Reorder the terms:
6 + -15 + -9x + -8x + 3x2 + -1x2 = 0

Combine like terms: 6 + -15 = -9
-9 + -9x + -8x + 3x2 + -1x2 = 0

Combine like terms: -9x + -8x = -17x
-9 + -17x + 3x2 + -1x2 = 0

Combine like terms: 3x2 + -1x2 = 2x2
-9 + -17x + 2x2 = 0

Solving
-9 + -17x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

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 = {-0.5, 9}

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