(8x+10)(10x+9)=0

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Solution for (8x+10)(10x+9)=0 equation: 


Simplifying
(8x + 10)(10x + 9) = 0

Reorder the terms:
(10 + 8x)(10x + 9) = 0

Reorder the terms:
(10 + 8x)(9 + 10x) = 0

Multiply (10 + 8x) * (9 + 10x)
(10(9 + 10x) + 8x * (9 + 10x)) = 0
((9 * 10 + 10x * 10) + 8x * (9 + 10x)) = 0
((90 + 100x) + 8x * (9 + 10x)) = 0
(90 + 100x + (9 * 8x + 10x * 8x)) = 0
(90 + 100x + (72x + 80x2)) = 0

Combine like terms: 100x + 72x = 172x
(90 + 172x + 80x2) = 0

Solving
90 + 172x + 80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + 86x + 40x2) = 0

Factor a trinomial.
2((5 + 4x)(9 + 10x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(9 + 10x)' equal to zero and attempt to solve:

Simplifying
9 + 10x = 0

Solving
9 + 10x = 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 + 10x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 10x = 0 + -9
10x = 0 + -9

Combine like terms: 0 + -9 = -9
10x = -9

Divide each side by '10'.
x = -0.9

Simplifying
x = -0.9
Solution
x = {-1.25, -0.9}

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