# 2x^2-24x=-2x^2-7x-18

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## Solution for 2x^2-24x=-2x^2-7x-18 equation:

Simplifying
2x2 + -24x = -2x2 + -7x + -18

Reorder the terms:
-24x + 2x2 = -2x2 + -7x + -18

Reorder the terms:
-24x + 2x2 = -18 + -7x + -2x2

Solving
-24x + 2x2 = -18 + -7x + -2x2

Solving for variable 'x'.

Reorder the terms:
18 + -24x + 7x + 2x2 + 2x2 = -18 + -7x + -2x2 + 18 + 7x + 2x2

Combine like terms: -24x + 7x = -17x
18 + -17x + 2x2 + 2x2 = -18 + -7x + -2x2 + 18 + 7x + 2x2

Combine like terms: 2x2 + 2x2 = 4x2
18 + -17x + 4x2 = -18 + -7x + -2x2 + 18 + 7x + 2x2

Reorder the terms:
18 + -17x + 4x2 = -18 + 18 + -7x + 7x + -2x2 + 2x2

Combine like terms: -18 + 18 = 0
18 + -17x + 4x2 = 0 + -7x + 7x + -2x2 + 2x2
18 + -17x + 4x2 = -7x + 7x + -2x2 + 2x2

Combine like terms: -7x + 7x = 0
18 + -17x + 4x2 = 0 + -2x2 + 2x2
18 + -17x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
18 + -17x + 4x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -4x) = 0

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2Set 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 = 2.25Solutionx = {2, 2.25}`