(2x-7)(4x+3)=-44x

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Solution for (2x-7)(4x+3)=-44x equation: 


Simplifying
(2x + -7)(4x + 3) = -44x

Reorder the terms:
(-7 + 2x)(4x + 3) = -44x

Reorder the terms:
(-7 + 2x)(3 + 4x) = -44x

Multiply (-7 + 2x) * (3 + 4x)
(-7(3 + 4x) + 2x * (3 + 4x)) = -44x
((3 * -7 + 4x * -7) + 2x * (3 + 4x)) = -44x
((-21 + -28x) + 2x * (3 + 4x)) = -44x
(-21 + -28x + (3 * 2x + 4x * 2x)) = -44x
(-21 + -28x + (6x + 8x2)) = -44x

Combine like terms: -28x + 6x = -22x
(-21 + -22x + 8x2) = -44x

Solving
-21 + -22x + 8x2 = -44x

Solving for variable 'x'.

Reorder the terms:
-21 + -22x + 44x + 8x2 = -44x + 44x

Combine like terms: -22x + 44x = 22x
-21 + 22x + 8x2 = -44x + 44x

Combine like terms: -44x + 44x = 0
-21 + 22x + 8x2 = 0

Factor a trinomial.
(-7 + -2x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-3.5, 0.75}

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