(4x+5)(10x+5)=0

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Solution for (4x+5)(10x+5)=0 equation: 


Simplifying
(4x + 5)(10x + 5) = 0

Reorder the terms:
(5 + 4x)(10x + 5) = 0

Reorder the terms:
(5 + 4x)(5 + 10x) = 0

Multiply (5 + 4x) * (5 + 10x)
(5(5 + 10x) + 4x * (5 + 10x)) = 0
((5 * 5 + 10x * 5) + 4x * (5 + 10x)) = 0
((25 + 50x) + 4x * (5 + 10x)) = 0
(25 + 50x + (5 * 4x + 10x * 4x)) = 0
(25 + 50x + (20x + 40x2)) = 0

Combine like terms: 50x + 20x = 70x
(25 + 70x + 40x2) = 0

Solving
25 + 70x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + 14x + 8x2) = 0

Factor a trinomial.
5((5 + 4x)(1 + 2x)) = 0

Ignore the factor 5.

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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.25, -0.5}

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