=(3x+7)(2x+1)+(x-4)(-2x-1)

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Solution for =(3x+7)(2x+1)+(x-4)(-2x-1) equation: 


Simplifying
0 = (3x + 7)(2x + 1) + (x + -4)(-2x + -1)

Reorder the terms:
0 = (7 + 3x)(2x + 1) + (x + -4)(-2x + -1)

Reorder the terms:
0 = (7 + 3x)(1 + 2x) + (x + -4)(-2x + -1)

Multiply (7 + 3x) * (1 + 2x)
0 = (7(1 + 2x) + 3x * (1 + 2x)) + (x + -4)(-2x + -1)
0 = ((1 * 7 + 2x * 7) + 3x * (1 + 2x)) + (x + -4)(-2x + -1)
0 = ((7 + 14x) + 3x * (1 + 2x)) + (x + -4)(-2x + -1)
0 = (7 + 14x + (1 * 3x + 2x * 3x)) + (x + -4)(-2x + -1)
0 = (7 + 14x + (3x + 6x2)) + (x + -4)(-2x + -1)

Combine like terms: 14x + 3x = 17x
0 = (7 + 17x + 6x2) + (x + -4)(-2x + -1)

Reorder the terms:
0 = 7 + 17x + 6x2 + (-4 + x)(-2x + -1)

Reorder the terms:
0 = 7 + 17x + 6x2 + (-4 + x)(-1 + -2x)

Multiply (-4 + x) * (-1 + -2x)
0 = 7 + 17x + 6x2 + (-4(-1 + -2x) + x(-1 + -2x))
0 = 7 + 17x + 6x2 + ((-1 * -4 + -2x * -4) + x(-1 + -2x))
0 = 7 + 17x + 6x2 + ((4 + 8x) + x(-1 + -2x))
0 = 7 + 17x + 6x2 + (4 + 8x + (-1 * x + -2x * x))
0 = 7 + 17x + 6x2 + (4 + 8x + (-1x + -2x2))

Combine like terms: 8x + -1x = 7x
0 = 7 + 17x + 6x2 + (4 + 7x + -2x2)

Reorder the terms:
0 = 7 + 4 + 17x + 7x + 6x2 + -2x2

Combine like terms: 7 + 4 = 11
0 = 11 + 17x + 7x + 6x2 + -2x2

Combine like terms: 17x + 7x = 24x
0 = 11 + 24x + 6x2 + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
0 = 11 + 24x + 4x2

Solving
0 = 11 + 24x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -11 = -11
-11 + -24x + -4x2 = 11 + 24x + 4x2 + -11 + -24x + -4x2

Reorder the terms:
-11 + -24x + -4x2 = 11 + -11 + 24x + -24x + 4x2 + -4x2

Combine like terms: 11 + -11 = 0
-11 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2
-11 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
-11 + -24x + -4x2 = 0 + 4x2 + -4x2
-11 + -24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-11 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 24x + 4x2) = 0

Factor a trinomial.
-1((11 + 2x)(1 + 2x)) = 0

Ignore the factor -1.

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 '(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 = {-5.5, -0.5}

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