(5x+2)(5x+2)+15x+6=0

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Solution for (5x+2)(5x+2)+15x+6=0 equation: 


Simplifying
(5x + 2)(5x + 2) + 15x + 6 = 0

Reorder the terms:
(2 + 5x)(5x + 2) + 15x + 6 = 0

Reorder the terms:
(2 + 5x)(2 + 5x) + 15x + 6 = 0

Multiply (2 + 5x) * (2 + 5x)
(2(2 + 5x) + 5x * (2 + 5x)) + 15x + 6 = 0
((2 * 2 + 5x * 2) + 5x * (2 + 5x)) + 15x + 6 = 0
((4 + 10x) + 5x * (2 + 5x)) + 15x + 6 = 0
(4 + 10x + (2 * 5x + 5x * 5x)) + 15x + 6 = 0
(4 + 10x + (10x + 25x2)) + 15x + 6 = 0

Combine like terms: 10x + 10x = 20x
(4 + 20x + 25x2) + 15x + 6 = 0

Reorder the terms:
4 + 6 + 20x + 15x + 25x2 = 0

Combine like terms: 4 + 6 = 10
10 + 20x + 15x + 25x2 = 0

Combine like terms: 20x + 15x = 35x
10 + 35x + 25x2 = 0

Solving
10 + 35x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 7x + 5x2) = 0

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

Ignore the factor 5.

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-1, -0.4}

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