x(9x+19)=4x^2-10x+42

Solution for x(9x+19)=4x^2-10x+42 equation:

Simplifying
x(9x + 19) = 4x2 + -10x + 42

Reorder the terms:
x(19 + 9x) = 4x2 + -10x + 42
(19 * x + 9x * x) = 4x2 + -10x + 42
(19x + 9x2) = 4x2 + -10x + 42

Reorder the terms:
19x + 9x2 = 42 + -10x + 4x2

Solving
19x + 9x2 = 42 + -10x + 4x2

Solving for variable 'x'.

Reorder the terms:
-42 + 19x + 10x + 9x2 + -4x2 = 42 + -10x + 4x2 + -42 + 10x + -4x2

Combine like terms: 19x + 10x = 29x
-42 + 29x + 9x2 + -4x2 = 42 + -10x + 4x2 + -42 + 10x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-42 + 29x + 5x2 = 42 + -10x + 4x2 + -42 + 10x + -4x2

Reorder the terms:
-42 + 29x + 5x2 = 42 + -42 + -10x + 10x + 4x2 + -4x2

Combine like terms: 42 + -42 = 0
-42 + 29x + 5x2 = 0 + -10x + 10x + 4x2 + -4x2
-42 + 29x + 5x2 = -10x + 10x + 4x2 + -4x2

Combine like terms: -10x + 10x = 0
-42 + 29x + 5x2 = 0 + 4x2 + -4x2
-42 + 29x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-42 + 29x + 5x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -5x) = 0

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-7, 1.2}