(5x+7)(7x-4)=0

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Solution for (5x+7)(7x-4)=0 equation: 


Simplifying
(5x + 7)(7x + -4) = 0

Reorder the terms:
(7 + 5x)(7x + -4) = 0

Reorder the terms:
(7 + 5x)(-4 + 7x) = 0

Multiply (7 + 5x) * (-4 + 7x)
(7(-4 + 7x) + 5x * (-4 + 7x)) = 0
((-4 * 7 + 7x * 7) + 5x * (-4 + 7x)) = 0
((-28 + 49x) + 5x * (-4 + 7x)) = 0
(-28 + 49x + (-4 * 5x + 7x * 5x)) = 0
(-28 + 49x + (-20x + 35x2)) = 0

Combine like terms: 49x + -20x = 29x
(-28 + 29x + 35x2) = 0

Solving
-28 + 29x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -5x)(4 + -7x) = 0


Subproblem 1
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

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 = {-1.4, 0.5714285714}

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