(5x-6)(3x-7)-(5x-6)(5x+6)=

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Solution for (5x-6)(3x-7)-(5x-6)(5x+6)= equation: 


Simplifying
(5x + -6)(3x + -7) + -1(5x + -6)(5x + 6) = 0

Reorder the terms:
(-6 + 5x)(3x + -7) + -1(5x + -6)(5x + 6) = 0

Reorder the terms:
(-6 + 5x)(-7 + 3x) + -1(5x + -6)(5x + 6) = 0

Multiply (-6 + 5x) * (-7 + 3x)
(-6(-7 + 3x) + 5x * (-7 + 3x)) + -1(5x + -6)(5x + 6) = 0
((-7 * -6 + 3x * -6) + 5x * (-7 + 3x)) + -1(5x + -6)(5x + 6) = 0
((42 + -18x) + 5x * (-7 + 3x)) + -1(5x + -6)(5x + 6) = 0
(42 + -18x + (-7 * 5x + 3x * 5x)) + -1(5x + -6)(5x + 6) = 0
(42 + -18x + (-35x + 15x2)) + -1(5x + -6)(5x + 6) = 0

Combine like terms: -18x + -35x = -53x
(42 + -53x + 15x2) + -1(5x + -6)(5x + 6) = 0

Reorder the terms:
42 + -53x + 15x2 + -1(-6 + 5x)(5x + 6) = 0

Reorder the terms:
42 + -53x + 15x2 + -1(-6 + 5x)(6 + 5x) = 0

Multiply (-6 + 5x) * (6 + 5x)
42 + -53x + 15x2 + -1(-6(6 + 5x) + 5x * (6 + 5x)) = 0
42 + -53x + 15x2 + -1((6 * -6 + 5x * -6) + 5x * (6 + 5x)) = 0
42 + -53x + 15x2 + -1((-36 + -30x) + 5x * (6 + 5x)) = 0
42 + -53x + 15x2 + -1(-36 + -30x + (6 * 5x + 5x * 5x)) = 0
42 + -53x + 15x2 + -1(-36 + -30x + (30x + 25x2)) = 0

Combine like terms: -30x + 30x = 0
42 + -53x + 15x2 + -1(-36 + 0 + 25x2) = 0
42 + -53x + 15x2 + -1(-36 + 25x2) = 0
42 + -53x + 15x2 + (-36 * -1 + 25x2 * -1) = 0
42 + -53x + 15x2 + (36 + -25x2) = 0

Reorder the terms:
42 + 36 + -53x + 15x2 + -25x2 = 0

Combine like terms: 42 + 36 = 78
78 + -53x + 15x2 + -25x2 = 0

Combine like terms: 15x2 + -25x2 = -10x2
78 + -53x + -10x2 = 0

Solving
78 + -53x + -10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -5x)(13 + 2x) = 0


Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2

Subproblem 2
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {1.2, -6.5}

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