25x^2-8x-24=(10)(x)(2x+5)

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Solution for 25x^2-8x-24=(10)(x)(2x+5) equation: 


Simplifying
25x2 + -8x + -24 = (10)(x)(2x + 5)

Reorder the terms:
-24 + -8x + 25x2 = (10)(x)(2x + 5)

Reorder the terms:
-24 + -8x + 25x2 = 10x(5 + 2x)
-24 + -8x + 25x2 = (5 * 10x + 2x * 10x)
-24 + -8x + 25x2 = (50x + 20x2)

Solving
-24 + -8x + 25x2 = 50x + 20x2

Solving for variable 'x'.

Reorder the terms:
-24 + -8x + -50x + 25x2 + -20x2 = 50x + 20x2 + -50x + -20x2

Combine like terms: -8x + -50x = -58x
-24 + -58x + 25x2 + -20x2 = 50x + 20x2 + -50x + -20x2

Combine like terms: 25x2 + -20x2 = 5x2
-24 + -58x + 5x2 = 50x + 20x2 + -50x + -20x2

Reorder the terms:
-24 + -58x + 5x2 = 50x + -50x + 20x2 + -20x2

Combine like terms: 50x + -50x = 0
-24 + -58x + 5x2 = 0 + 20x2 + -20x2
-24 + -58x + 5x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-24 + -58x + 5x2 = 0

Factor a trinomial.
(-2 + -5x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-0.4, 12}

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