(x-5)(x-3)-(6x-4)(x+3)=

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Solution for (x-5)(x-3)-(6x-4)(x+3)= equation: 


Simplifying
(x + -5)(x + -3) + -1(6x + -4)(x + 3) = 0

Reorder the terms:
(-5 + x)(x + -3) + -1(6x + -4)(x + 3) = 0

Reorder the terms:
(-5 + x)(-3 + x) + -1(6x + -4)(x + 3) = 0

Multiply (-5 + x) * (-3 + x)
(-5(-3 + x) + x(-3 + x)) + -1(6x + -4)(x + 3) = 0
((-3 * -5 + x * -5) + x(-3 + x)) + -1(6x + -4)(x + 3) = 0
((15 + -5x) + x(-3 + x)) + -1(6x + -4)(x + 3) = 0
(15 + -5x + (-3 * x + x * x)) + -1(6x + -4)(x + 3) = 0
(15 + -5x + (-3x + x2)) + -1(6x + -4)(x + 3) = 0

Combine like terms: -5x + -3x = -8x
(15 + -8x + x2) + -1(6x + -4)(x + 3) = 0

Reorder the terms:
15 + -8x + x2 + -1(-4 + 6x)(x + 3) = 0

Reorder the terms:
15 + -8x + x2 + -1(-4 + 6x)(3 + x) = 0

Multiply (-4 + 6x) * (3 + x)
15 + -8x + x2 + -1(-4(3 + x) + 6x * (3 + x)) = 0
15 + -8x + x2 + -1((3 * -4 + x * -4) + 6x * (3 + x)) = 0
15 + -8x + x2 + -1((-12 + -4x) + 6x * (3 + x)) = 0
15 + -8x + x2 + -1(-12 + -4x + (3 * 6x + x * 6x)) = 0
15 + -8x + x2 + -1(-12 + -4x + (18x + 6x2)) = 0

Combine like terms: -4x + 18x = 14x
15 + -8x + x2 + -1(-12 + 14x + 6x2) = 0
15 + -8x + x2 + (-12 * -1 + 14x * -1 + 6x2 * -1) = 0
15 + -8x + x2 + (12 + -14x + -6x2) = 0

Reorder the terms:
15 + 12 + -8x + -14x + x2 + -6x2 = 0

Combine like terms: 15 + 12 = 27
27 + -8x + -14x + x2 + -6x2 = 0

Combine like terms: -8x + -14x = -22x
27 + -22x + x2 + -6x2 = 0

Combine like terms: x2 + -6x2 = -5x2
27 + -22x + -5x2 = 0

Solving
27 + -22x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(27 + 5x) = 0


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 '(27 + 5x)' equal to zero and attempt to solve:

Simplifying
27 + 5x = 0

Solving
27 + 5x = 0

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

Add '-27' to each side of the equation.
27 + -27 + 5x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 5x = 0 + -27
5x = 0 + -27

Combine like terms: 0 + -27 = -27
5x = -27

Divide each side by '5'.
x = -5.4

Simplifying
x = -5.4
Solution
x = {1, -5.4}

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