(10x+17)(7x-4)=0

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Solution for (10x+17)(7x-4)=0 equation: 


Simplifying
(10x + 17)(7x + -4) = 0

Reorder the terms:
(17 + 10x)(7x + -4) = 0

Reorder the terms:
(17 + 10x)(-4 + 7x) = 0

Multiply (17 + 10x) * (-4 + 7x)
(17(-4 + 7x) + 10x * (-4 + 7x)) = 0
((-4 * 17 + 7x * 17) + 10x * (-4 + 7x)) = 0
((-68 + 119x) + 10x * (-4 + 7x)) = 0
(-68 + 119x + (-4 * 10x + 7x * 10x)) = 0
(-68 + 119x + (-40x + 70x2)) = 0

Combine like terms: 119x + -40x = 79x
(-68 + 79x + 70x2) = 0

Solving
-68 + 79x + 70x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -10x)(4 + -7x) = 0


Subproblem 1
Set the factor '(-17 + -10x)' equal to zero and attempt to solve:

Simplifying
-17 + -10x = 0

Solving
-17 + -10x = 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 + -10x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -10x = 0 + 17
-10x = 0 + 17

Combine like terms: 0 + 17 = 17
-10x = 17

Divide each side by '-10'.
x = -1.7

Simplifying
x = -1.7

Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {-1.7, 0.5714285714}

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