25-16x^2=12x(x+5)

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Solution for 25-16x^2=12x(x+5) equation: 


Simplifying
25 + -16x2 = 12x(x + 5)

Reorder the terms:
25 + -16x2 = 12x(5 + x)
25 + -16x2 = (5 * 12x + x * 12x)
25 + -16x2 = (60x + 12x2)

Solving
25 + -16x2 = 60x + 12x2

Solving for variable 'x'.

Reorder the terms:
25 + -60x + -16x2 + -12x2 = 60x + 12x2 + -60x + -12x2

Combine like terms: -16x2 + -12x2 = -28x2
25 + -60x + -28x2 = 60x + 12x2 + -60x + -12x2

Reorder the terms:
25 + -60x + -28x2 = 60x + -60x + 12x2 + -12x2

Combine like terms: 60x + -60x = 0
25 + -60x + -28x2 = 0 + 12x2 + -12x2
25 + -60x + -28x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
25 + -60x + -28x2 = 0

Factor a trinomial.
(5 + -14x)(5 + 2x) = 0


Subproblem 1
Set the factor '(5 + -14x)' equal to zero and attempt to solve:

Simplifying
5 + -14x = 0

Solving
5 + -14x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -14x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -14x = 0 + -5
-14x = 0 + -5

Combine like terms: 0 + -5 = -5
-14x = -5

Divide each side by '-14'.
x = 0.3571428571

Simplifying
x = 0.3571428571

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0.3571428571, -2.5}

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