4x^2-11x+15=9x+6

Solution for 4x^2-11x+15=9x+6 equation:

Simplifying
4x2 + -11x + 15 = 9x + 6

Reorder the terms:
15 + -11x + 4x2 = 9x + 6

Reorder the terms:
15 + -11x + 4x2 = 6 + 9x

Solving
15 + -11x + 4x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
15 + -6 + -11x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: 15 + -6 = 9
9 + -11x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: -11x + -9x = -20x
9 + -20x + 4x2 = 6 + 9x + -6 + -9x

Reorder the terms:
9 + -20x + 4x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
9 + -20x + 4x2 = 0 + 9x + -9x
9 + -20x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
9 + -20x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(9 + -2x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {0.5, 4.5}