(8x+10)(2x+7)=0

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Solution for (8x+10)(2x+7)=0 equation: 


Simplifying
(8x + 10)(2x + 7) = 0

Reorder the terms:
(10 + 8x)(2x + 7) = 0

Reorder the terms:
(10 + 8x)(7 + 2x) = 0

Multiply (10 + 8x) * (7 + 2x)
(10(7 + 2x) + 8x * (7 + 2x)) = 0
((7 * 10 + 2x * 10) + 8x * (7 + 2x)) = 0
((70 + 20x) + 8x * (7 + 2x)) = 0
(70 + 20x + (7 * 8x + 2x * 8x)) = 0
(70 + 20x + (56x + 16x2)) = 0

Combine like terms: 20x + 56x = 76x
(70 + 76x + 16x2) = 0

Solving
70 + 76x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + 38x + 8x2) = 0

Factor a trinomial.
2((7 + 2x)(5 + 4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
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
Solution
x = {-3.5, -1.25}

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