2x^2+9x=4x+42

Solution for 2x^2+9x=4x+42 equation:

Simplifying
2x2 + 9x = 4x + 42

Reorder the terms:
9x + 2x2 = 4x + 42

Reorder the terms:
9x + 2x2 = 42 + 4x

Solving
9x + 2x2 = 42 + 4x

Solving for variable 'x'.

Reorder the terms:
-42 + 9x + -4x + 2x2 = 42 + 4x + -42 + -4x

Combine like terms: 9x + -4x = 5x
-42 + 5x + 2x2 = 42 + 4x + -42 + -4x

Reorder the terms:
-42 + 5x + 2x2 = 42 + -42 + 4x + -4x

Combine like terms: 42 + -42 = 0
-42 + 5x + 2x2 = 0 + 4x + -4x
-42 + 5x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-42 + 5x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -2x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 3.5}