(5x-14)(4x-17)=0

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Solution for (5x-14)(4x-17)=0 equation: 


Simplifying
(5x + -14)(4x + -17) = 0

Reorder the terms:
(-14 + 5x)(4x + -17) = 0

Reorder the terms:
(-14 + 5x)(-17 + 4x) = 0

Multiply (-14 + 5x) * (-17 + 4x)
(-14(-17 + 4x) + 5x * (-17 + 4x)) = 0
((-17 * -14 + 4x * -14) + 5x * (-17 + 4x)) = 0
((238 + -56x) + 5x * (-17 + 4x)) = 0
(238 + -56x + (-17 * 5x + 4x * 5x)) = 0
(238 + -56x + (-85x + 20x2)) = 0

Combine like terms: -56x + -85x = -141x
(238 + -141x + 20x2) = 0

Solving
238 + -141x + 20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(14 + -5x)(17 + -4x) = 0


Subproblem 1
Set the factor '(14 + -5x)' equal to zero and attempt to solve:

Simplifying
14 + -5x = 0

Solving
14 + -5x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -5x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -5x = 0 + -14
-5x = 0 + -14

Combine like terms: 0 + -14 = -14
-5x = -14

Divide each side by '-5'.
x = 2.8

Simplifying
x = 2.8

Subproblem 2
Set the factor '(17 + -4x)' equal to zero and attempt to solve:

Simplifying
17 + -4x = 0

Solving
17 + -4x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4x = 0 + -17
-4x = 0 + -17

Combine like terms: 0 + -17 = -17
-4x = -17

Divide each side by '-4'.
x = 4.25

Simplifying
x = 4.25
Solution
x = {2.8, 4.25}

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