5x^2-24x+7=2x^2-4x-5

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Solution for 5x^2-24x+7=2x^2-4x-5 equation: 


Simplifying
5x2 + -24x + 7 = 2x2 + -4x + -5

Reorder the terms:
7 + -24x + 5x2 = 2x2 + -4x + -5

Reorder the terms:
7 + -24x + 5x2 = -5 + -4x + 2x2

Solving
7 + -24x + 5x2 = -5 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
7 + 5 + -24x + 4x + 5x2 + -2x2 = -5 + -4x + 2x2 + 5 + 4x + -2x2

Combine like terms: 7 + 5 = 12
12 + -24x + 4x + 5x2 + -2x2 = -5 + -4x + 2x2 + 5 + 4x + -2x2

Combine like terms: -24x + 4x = -20x
12 + -20x + 5x2 + -2x2 = -5 + -4x + 2x2 + 5 + 4x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
12 + -20x + 3x2 = -5 + -4x + 2x2 + 5 + 4x + -2x2

Reorder the terms:
12 + -20x + 3x2 = -5 + 5 + -4x + 4x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
12 + -20x + 3x2 = 0 + -4x + 4x + 2x2 + -2x2
12 + -20x + 3x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
12 + -20x + 3x2 = 0 + 2x2 + -2x2
12 + -20x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -20x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(6 + -1x) = 0


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.6666666667, 6}

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