2x^2-24x=-2x^2-9x-14

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Solution for 2x^2-24x=-2x^2-9x-14 equation: 


Simplifying
2x2 + -24x = -2x2 + -9x + -14

Reorder the terms:
-24x + 2x2 = -2x2 + -9x + -14

Reorder the terms:
-24x + 2x2 = -14 + -9x + -2x2

Solving
-24x + 2x2 = -14 + -9x + -2x2

Solving for variable 'x'.

Reorder the terms:
14 + -24x + 9x + 2x2 + 2x2 = -14 + -9x + -2x2 + 14 + 9x + 2x2

Combine like terms: -24x + 9x = -15x
14 + -15x + 2x2 + 2x2 = -14 + -9x + -2x2 + 14 + 9x + 2x2

Combine like terms: 2x2 + 2x2 = 4x2
14 + -15x + 4x2 = -14 + -9x + -2x2 + 14 + 9x + 2x2

Reorder the terms:
14 + -15x + 4x2 = -14 + 14 + -9x + 9x + -2x2 + 2x2

Combine like terms: -14 + 14 = 0
14 + -15x + 4x2 = 0 + -9x + 9x + -2x2 + 2x2
14 + -15x + 4x2 = -9x + 9x + -2x2 + 2x2

Combine like terms: -9x + 9x = 0
14 + -15x + 4x2 = 0 + -2x2 + 2x2
14 + -15x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
14 + -15x + 4x2 = 0

Factor a trinomial.
(7 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

Subproblem 2
Set 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
Solution
x = {1.75, 2}

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