(9x-5)(4x-6)-(5x-6)(6x-4)+(x+1)(1-3x)=-2x^2-5x-3

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Solution for (9x-5)(4x-6)-(5x-6)(6x-4)+(x+1)(1-3x)=-2x^2-5x-3 equation: 


Simplifying
(9x + -5)(4x + -6) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Reorder the terms:
(-5 + 9x)(4x + -6) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Reorder the terms:
(-5 + 9x)(-6 + 4x) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Multiply (-5 + 9x) * (-6 + 4x)
(-5(-6 + 4x) + 9x * (-6 + 4x)) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
((-6 * -5 + 4x * -5) + 9x * (-6 + 4x)) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
((30 + -20x) + 9x * (-6 + 4x)) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
(30 + -20x + (-6 * 9x + 4x * 9x)) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
(30 + -20x + (-54x + 36x2)) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Combine like terms: -20x + -54x = -74x
(30 + -74x + 36x2) + -1(5x + -6)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Reorder the terms:
30 + -74x + 36x2 + -1(-6 + 5x)(6x + -4) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Reorder the terms:
30 + -74x + 36x2 + -1(-6 + 5x)(-4 + 6x) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Multiply (-6 + 5x) * (-4 + 6x)
30 + -74x + 36x2 + -1(-6(-4 + 6x) + 5x * (-4 + 6x)) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + -1((-4 * -6 + 6x * -6) + 5x * (-4 + 6x)) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + -1((24 + -36x) + 5x * (-4 + 6x)) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + -1(24 + -36x + (-4 * 5x + 6x * 5x)) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + -1(24 + -36x + (-20x + 30x2)) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Combine like terms: -36x + -20x = -56x
30 + -74x + 36x2 + -1(24 + -56x + 30x2) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + (24 * -1 + -56x * -1 + 30x2 * -1) + (x + 1)(1 + -3x) = -2x2 + -5x + -3
30 + -74x + 36x2 + (-24 + 56x + -30x2) + (x + 1)(1 + -3x) = -2x2 + -5x + -3

Reorder the terms:
30 + -74x + 36x2 + -24 + 56x + -30x2 + (1 + x)(1 + -3x) = -2x2 + -5x + -3

Multiply (1 + x) * (1 + -3x)
30 + -74x + 36x2 + -24 + 56x + -30x2 + (1(1 + -3x) + x(1 + -3x)) = -2x2 + -5x + -3
30 + -74x + 36x2 + -24 + 56x + -30x2 + ((1 * 1 + -3x * 1) + x(1 + -3x)) = -2x2 + -5x + -3
30 + -74x + 36x2 + -24 + 56x + -30x2 + ((1 + -3x) + x(1 + -3x)) = -2x2 + -5x + -3
30 + -74x + 36x2 + -24 + 56x + -30x2 + (1 + -3x + (1 * x + -3x * x)) = -2x2 + -5x + -3
30 + -74x + 36x2 + -24 + 56x + -30x2 + (1 + -3x + (1x + -3x2)) = -2x2 + -5x + -3

Combine like terms: -3x + 1x = -2x
30 + -74x + 36x2 + -24 + 56x + -30x2 + (1 + -2x + -3x2) = -2x2 + -5x + -3

Reorder the terms:
30 + -24 + 1 + -74x + 56x + -2x + 36x2 + -30x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: 30 + -24 = 6
6 + 1 + -74x + 56x + -2x + 36x2 + -30x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: 6 + 1 = 7
7 + -74x + 56x + -2x + 36x2 + -30x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: -74x + 56x = -18x
7 + -18x + -2x + 36x2 + -30x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: -18x + -2x = -20x
7 + -20x + 36x2 + -30x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: 36x2 + -30x2 = 6x2
7 + -20x + 6x2 + -3x2 = -2x2 + -5x + -3

Combine like terms: 6x2 + -3x2 = 3x2
7 + -20x + 3x2 = -2x2 + -5x + -3

Reorder the terms:
7 + -20x + 3x2 = -3 + -5x + -2x2

Solving
7 + -20x + 3x2 = -3 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
7 + 3 + -20x + 5x + 3x2 + 2x2 = -3 + -5x + -2x2 + 3 + 5x + 2x2

Combine like terms: 7 + 3 = 10
10 + -20x + 5x + 3x2 + 2x2 = -3 + -5x + -2x2 + 3 + 5x + 2x2

Combine like terms: -20x + 5x = -15x
10 + -15x + 3x2 + 2x2 = -3 + -5x + -2x2 + 3 + 5x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
10 + -15x + 5x2 = -3 + -5x + -2x2 + 3 + 5x + 2x2

Reorder the terms:
10 + -15x + 5x2 = -3 + 3 + -5x + 5x + -2x2 + 2x2

Combine like terms: -3 + 3 = 0
10 + -15x + 5x2 = 0 + -5x + 5x + -2x2 + 2x2
10 + -15x + 5x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
10 + -15x + 5x2 = 0 + -2x2 + 2x2
10 + -15x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10 + -15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -3x + x2) = 0

Factor a trinomial.
5((1 + -1x)(2 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 2}

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