4x^2-5x+15=8x+6

Solution for 4x^2-5x+15=8x+6 equation:

Simplifying
4x2 + -5x + 15 = 8x + 6

Reorder the terms:
15 + -5x + 4x2 = 8x + 6

Reorder the terms:
15 + -5x + 4x2 = 6 + 8x

Solving
15 + -5x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
15 + -6 + -5x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: 15 + -6 = 9
9 + -5x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -5x + -8x = -13x
9 + -13x + 4x2 = 6 + 8x + -6 + -8x

Reorder the terms:
9 + -13x + 4x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
9 + -13x + 4x2 = 0 + 8x + -8x
9 + -13x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
9 + -13x + 4x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -4x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

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

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

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {1, 2.25}