(2x-9)(7x+8)=0

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Solution for (2x-9)(7x+8)=0 equation: 


Simplifying
(2x + -9)(7x + 8) = 0

Reorder the terms:
(-9 + 2x)(7x + 8) = 0

Reorder the terms:
(-9 + 2x)(8 + 7x) = 0

Multiply (-9 + 2x) * (8 + 7x)
(-9(8 + 7x) + 2x * (8 + 7x)) = 0
((8 * -9 + 7x * -9) + 2x * (8 + 7x)) = 0
((-72 + -63x) + 2x * (8 + 7x)) = 0
(-72 + -63x + (8 * 2x + 7x * 2x)) = 0
(-72 + -63x + (16x + 14x2)) = 0

Combine like terms: -63x + 16x = -47x
(-72 + -47x + 14x2) = 0

Solving
-72 + -47x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(9 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 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 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

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

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-1.142857143, 4.5}

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