(4x+3)(x+3)=-5x

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Solution for (4x+3)(x+3)=-5x equation: 


Simplifying
(4x + 3)(x + 3) = -5x

Reorder the terms:
(3 + 4x)(x + 3) = -5x

Reorder the terms:
(3 + 4x)(3 + x) = -5x

Multiply (3 + 4x) * (3 + x)
(3(3 + x) + 4x * (3 + x)) = -5x
((3 * 3 + x * 3) + 4x * (3 + x)) = -5x
((9 + 3x) + 4x * (3 + x)) = -5x
(9 + 3x + (3 * 4x + x * 4x)) = -5x
(9 + 3x + (12x + 4x2)) = -5x

Combine like terms: 3x + 12x = 15x
(9 + 15x + 4x2) = -5x

Solving
9 + 15x + 4x2 = -5x

Solving for variable 'x'.

Reorder the terms:
9 + 15x + 5x + 4x2 = -5x + 5x

Combine like terms: 15x + 5x = 20x
9 + 20x + 4x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
9 + 20x + 4x2 = 0

Factor a trinomial.
(9 + 2x)(1 + 2x) = 0


Subproblem 1
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

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 = {-4.5, -0.5}

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