(4x-1)(x+5)=11x+16

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Solution for (4x-1)(x+5)=11x+16 equation: 


Simplifying
(4x + -1)(x + 5) = 11x + 16

Reorder the terms:
(-1 + 4x)(x + 5) = 11x + 16

Reorder the terms:
(-1 + 4x)(5 + x) = 11x + 16

Multiply (-1 + 4x) * (5 + x)
(-1(5 + x) + 4x * (5 + x)) = 11x + 16
((5 * -1 + x * -1) + 4x * (5 + x)) = 11x + 16
((-5 + -1x) + 4x * (5 + x)) = 11x + 16
(-5 + -1x + (5 * 4x + x * 4x)) = 11x + 16
(-5 + -1x + (20x + 4x2)) = 11x + 16

Combine like terms: -1x + 20x = 19x
(-5 + 19x + 4x2) = 11x + 16

Reorder the terms:
-5 + 19x + 4x2 = 16 + 11x

Solving
-5 + 19x + 4x2 = 16 + 11x

Solving for variable 'x'.

Reorder the terms:
-5 + -16 + 19x + -11x + 4x2 = 16 + 11x + -16 + -11x

Combine like terms: -5 + -16 = -21
-21 + 19x + -11x + 4x2 = 16 + 11x + -16 + -11x

Combine like terms: 19x + -11x = 8x
-21 + 8x + 4x2 = 16 + 11x + -16 + -11x

Reorder the terms:
-21 + 8x + 4x2 = 16 + -16 + 11x + -11x

Combine like terms: 16 + -16 = 0
-21 + 8x + 4x2 = 0 + 11x + -11x
-21 + 8x + 4x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-21 + 8x + 4x2 = 0

Factor a trinomial.
(-7 + -2x)(3 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3.5, 1.5}

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