(4x+11)(2x-8)=x(2x+7)

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Solution for (4x+11)(2x-8)=x(2x+7) equation: 


Simplifying
(4x + 11)(2x + -8) = x(2x + 7)

Reorder the terms:
(11 + 4x)(2x + -8) = x(2x + 7)

Reorder the terms:
(11 + 4x)(-8 + 2x) = x(2x + 7)

Multiply (11 + 4x) * (-8 + 2x)
(11(-8 + 2x) + 4x * (-8 + 2x)) = x(2x + 7)
((-8 * 11 + 2x * 11) + 4x * (-8 + 2x)) = x(2x + 7)
((-88 + 22x) + 4x * (-8 + 2x)) = x(2x + 7)
(-88 + 22x + (-8 * 4x + 2x * 4x)) = x(2x + 7)
(-88 + 22x + (-32x + 8x2)) = x(2x + 7)

Combine like terms: 22x + -32x = -10x
(-88 + -10x + 8x2) = x(2x + 7)

Reorder the terms:
-88 + -10x + 8x2 = x(7 + 2x)
-88 + -10x + 8x2 = (7 * x + 2x * x)
-88 + -10x + 8x2 = (7x + 2x2)

Solving
-88 + -10x + 8x2 = 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-88 + -10x + -7x + 8x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: -10x + -7x = -17x
-88 + -17x + 8x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-88 + -17x + 6x2 = 7x + 2x2 + -7x + -2x2

Reorder the terms:
-88 + -17x + 6x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-88 + -17x + 6x2 = 0 + 2x2 + -2x2
-88 + -17x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-88 + -17x + 6x2 = 0

Factor a trinomial.
(-8 + -3x)(11 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
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
Solution
x = {-2.666666667, 5.5}

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