(5x+8)(7x-9)=0

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Solution for (5x+8)(7x-9)=0 equation: 


Simplifying
(5x + 8)(7x + -9) = 0

Reorder the terms:
(8 + 5x)(7x + -9) = 0

Reorder the terms:
(8 + 5x)(-9 + 7x) = 0

Multiply (8 + 5x) * (-9 + 7x)
(8(-9 + 7x) + 5x * (-9 + 7x)) = 0
((-9 * 8 + 7x * 8) + 5x * (-9 + 7x)) = 0
((-72 + 56x) + 5x * (-9 + 7x)) = 0
(-72 + 56x + (-9 * 5x + 7x * 5x)) = 0
(-72 + 56x + (-45x + 35x2)) = 0

Combine like terms: 56x + -45x = 11x
(-72 + 11x + 35x2) = 0

Solving
-72 + 11x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -5x)(9 + -7x) = 0


Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6

Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-1.6, 1.285714286}

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