(x+3)(2x-1)=4(x^2-9)

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Solution for (x+3)(2x-1)=4(x^2-9) equation: 


Simplifying
(x + 3)(2x + -1) = 4(x2 + -9)

Reorder the terms:
(3 + x)(2x + -1) = 4(x2 + -9)

Reorder the terms:
(3 + x)(-1 + 2x) = 4(x2 + -9)

Multiply (3 + x) * (-1 + 2x)
(3(-1 + 2x) + x(-1 + 2x)) = 4(x2 + -9)
((-1 * 3 + 2x * 3) + x(-1 + 2x)) = 4(x2 + -9)
((-3 + 6x) + x(-1 + 2x)) = 4(x2 + -9)
(-3 + 6x + (-1 * x + 2x * x)) = 4(x2 + -9)
(-3 + 6x + (-1x + 2x2)) = 4(x2 + -9)

Combine like terms: 6x + -1x = 5x
(-3 + 5x + 2x2) = 4(x2 + -9)

Reorder the terms:
-3 + 5x + 2x2 = 4(-9 + x2)
-3 + 5x + 2x2 = (-9 * 4 + x2 * 4)
-3 + 5x + 2x2 = (-36 + 4x2)

Solving
-3 + 5x + 2x2 = -36 + 4x2

Solving for variable 'x'.

Reorder the terms:
-3 + 36 + 5x + 2x2 + -4x2 = -36 + 4x2 + 36 + -4x2

Combine like terms: -3 + 36 = 33
33 + 5x + 2x2 + -4x2 = -36 + 4x2 + 36 + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
33 + 5x + -2x2 = -36 + 4x2 + 36 + -4x2

Reorder the terms:
33 + 5x + -2x2 = -36 + 36 + 4x2 + -4x2

Combine like terms: -36 + 36 = 0
33 + 5x + -2x2 = 0 + 4x2 + -4x2
33 + 5x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
33 + 5x + -2x2 = 0

Factor a trinomial.
(11 + -2x)(3 + x) = 0


Subproblem 1
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5

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 = {5.5, -3}

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