(5x-7)(6-2x)-(3x-7)(5x-7)=0

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Solution for (5x-7)(6-2x)-(3x-7)(5x-7)=0 equation:


Simplifying
(5x + -7)(6 + -2x) + -1(3x + -7)(5x + -7) = 0

Reorder the terms:
(-7 + 5x)(6 + -2x) + -1(3x + -7)(5x + -7) = 0

Multiply (-7 + 5x) * (6 + -2x)
(-7(6 + -2x) + 5x * (6 + -2x)) + -1(3x + -7)(5x + -7) = 0
((6 * -7 + -2x * -7) + 5x * (6 + -2x)) + -1(3x + -7)(5x + -7) = 0
((-42 + 14x) + 5x * (6 + -2x)) + -1(3x + -7)(5x + -7) = 0
(-42 + 14x + (6 * 5x + -2x * 5x)) + -1(3x + -7)(5x + -7) = 0
(-42 + 14x + (30x + -10x2)) + -1(3x + -7)(5x + -7) = 0

Combine like terms: 14x + 30x = 44x
(-42 + 44x + -10x2) + -1(3x + -7)(5x + -7) = 0

Reorder the terms:
-42 + 44x + -10x2 + -1(-7 + 3x)(5x + -7) = 0

Reorder the terms:
-42 + 44x + -10x2 + -1(-7 + 3x)(-7 + 5x) = 0

Multiply (-7 + 3x) * (-7 + 5x)
-42 + 44x + -10x2 + -1(-7(-7 + 5x) + 3x * (-7 + 5x)) = 0
-42 + 44x + -10x2 + -1((-7 * -7 + 5x * -7) + 3x * (-7 + 5x)) = 0
-42 + 44x + -10x2 + -1((49 + -35x) + 3x * (-7 + 5x)) = 0
-42 + 44x + -10x2 + -1(49 + -35x + (-7 * 3x + 5x * 3x)) = 0
-42 + 44x + -10x2 + -1(49 + -35x + (-21x + 15x2)) = 0

Combine like terms: -35x + -21x = -56x
-42 + 44x + -10x2 + -1(49 + -56x + 15x2) = 0
-42 + 44x + -10x2 + (49 * -1 + -56x * -1 + 15x2 * -1) = 0
-42 + 44x + -10x2 + (-49 + 56x + -15x2) = 0

Reorder the terms:
-42 + -49 + 44x + 56x + -10x2 + -15x2 = 0

Combine like terms: -42 + -49 = -91
-91 + 44x + 56x + -10x2 + -15x2 = 0

Combine like terms: 44x + 56x = 100x
-91 + 100x + -10x2 + -15x2 = 0

Combine like terms: -10x2 + -15x2 = -25x2
-91 + 100x + -25x2 = 0

Solving
-91 + 100x + -25x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + 5x)(7 + -5x) = 0


Subproblem 1
Set the factor '(-13 + 5x)' equal to zero and attempt to solve:

Simplifying
-13 + 5x = 0

Solving
-13 + 5x = 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 + 5x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 5x = 0 + 13
5x = 0 + 13

Combine like terms: 0 + 13 = 13
5x = 13

Divide each side by '5'.
x = 2.6

Simplifying
x = 2.6

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {2.6, 1.4}

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