4x(4x+5)=19x+19-3x+1

Solution for 4x(4x+5)=19x+19-3x+1 equation:

Simplifying
4x(4x + 5) = 19x + 19 + -3x + 1

Reorder the terms:
4x(5 + 4x) = 19x + 19 + -3x + 1
(5 * 4x + 4x * 4x) = 19x + 19 + -3x + 1
(20x + 16x2) = 19x + 19 + -3x + 1

Reorder the terms:
20x + 16x2 = 19 + 1 + 19x + -3x

Combine like terms: 19 + 1 = 20
20x + 16x2 = 20 + 19x + -3x

Combine like terms: 19x + -3x = 16x
20x + 16x2 = 20 + 16x

Solving
20x + 16x2 = 20 + 16x

Solving for variable 'x'.

Reorder the terms:
-20 + 20x + -16x + 16x2 = 20 + 16x + -20 + -16x

Combine like terms: 20x + -16x = 4x
-20 + 4x + 16x2 = 20 + 16x + -20 + -16x

Reorder the terms:
-20 + 4x + 16x2 = 20 + -20 + 16x + -16x

Combine like terms: 20 + -20 = 0
-20 + 4x + 16x2 = 0 + 16x + -16x
-20 + 4x + 16x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-20 + 4x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + x + 4x2) = 0

Factor a trinomial.
4((-5 + -4x)(1 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.25, 1}