(2x+4)(2x+9)=3x^2+11x

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Solution for (2x+4)(2x+9)=3x^2+11x equation: 


Simplifying
(2x + 4)(2x + 9) = 3x2 + 11x

Reorder the terms:
(4 + 2x)(2x + 9) = 3x2 + 11x

Reorder the terms:
(4 + 2x)(9 + 2x) = 3x2 + 11x

Multiply (4 + 2x) * (9 + 2x)
(4(9 + 2x) + 2x * (9 + 2x)) = 3x2 + 11x
((9 * 4 + 2x * 4) + 2x * (9 + 2x)) = 3x2 + 11x
((36 + 8x) + 2x * (9 + 2x)) = 3x2 + 11x
(36 + 8x + (9 * 2x + 2x * 2x)) = 3x2 + 11x
(36 + 8x + (18x + 4x2)) = 3x2 + 11x

Combine like terms: 8x + 18x = 26x
(36 + 26x + 4x2) = 3x2 + 11x

Reorder the terms:
36 + 26x + 4x2 = 11x + 3x2

Solving
36 + 26x + 4x2 = 11x + 3x2

Solving for variable 'x'.

Reorder the terms:
36 + 26x + -11x + 4x2 + -3x2 = 11x + 3x2 + -11x + -3x2

Combine like terms: 26x + -11x = 15x
36 + 15x + 4x2 + -3x2 = 11x + 3x2 + -11x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
36 + 15x + 1x2 = 11x + 3x2 + -11x + -3x2

Reorder the terms:
36 + 15x + 1x2 = 11x + -11x + 3x2 + -3x2

Combine like terms: 11x + -11x = 0
36 + 15x + 1x2 = 0 + 3x2 + -3x2
36 + 15x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
36 + 15x + 1x2 = 0

Factor a trinomial.
(12 + x)(3 + x) = 0


Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-12, -3}

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