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

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


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

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

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

Multiply (-6 + 5x) * (-7 + 2x)
(-6(-7 + 2x) + 5x * (-7 + 2x)) = 0
((-7 * -6 + 2x * -6) + 5x * (-7 + 2x)) = 0
((42 + -12x) + 5x * (-7 + 2x)) = 0
(42 + -12x + (-7 * 5x + 2x * 5x)) = 0
(42 + -12x + (-35x + 10x2)) = 0

Combine like terms: -12x + -35x = -47x
(42 + -47x + 10x2) = 0

Solving
42 + -47x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -5x)(7 + -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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1.2, 3.5}

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