2x^2-24x=-3x^2-7x-6

Solution for 2x^2-24x=-3x^2-7x-6 equation:

Simplifying
2x2 + -24x = -3x2 + -7x + -6

Reorder the terms:
-24x + 2x2 = -3x2 + -7x + -6

Reorder the terms:
-24x + 2x2 = -6 + -7x + -3x2

Solving
-24x + 2x2 = -6 + -7x + -3x2

Solving for variable 'x'.

Reorder the terms:
6 + -24x + 7x + 2x2 + 3x2 = -6 + -7x + -3x2 + 6 + 7x + 3x2

Combine like terms: -24x + 7x = -17x
6 + -17x + 2x2 + 3x2 = -6 + -7x + -3x2 + 6 + 7x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
6 + -17x + 5x2 = -6 + -7x + -3x2 + 6 + 7x + 3x2

Reorder the terms:
6 + -17x + 5x2 = -6 + 6 + -7x + 7x + -3x2 + 3x2

Combine like terms: -6 + 6 = 0
6 + -17x + 5x2 = 0 + -7x + 7x + -3x2 + 3x2
6 + -17x + 5x2 = -7x + 7x + -3x2 + 3x2

Combine like terms: -7x + 7x = 0
6 + -17x + 5x2 = 0 + -3x2 + 3x2
6 + -17x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
6 + -17x + 5x2 = 0

Factor a trinomial.
(2 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.4, 3}