6x^2-1=25(x+2)

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Solution for 6x^2-1=25(x+2) equation: 


Simplifying
6x2 + -1 = 25(x + 2)

Reorder the terms:
-1 + 6x2 = 25(x + 2)

Reorder the terms:
-1 + 6x2 = 25(2 + x)
-1 + 6x2 = (2 * 25 + x * 25)
-1 + 6x2 = (50 + 25x)

Solving
-1 + 6x2 = 50 + 25x

Solving for variable 'x'.

Reorder the terms:
-1 + -50 + -25x + 6x2 = 50 + 25x + -50 + -25x

Combine like terms: -1 + -50 = -51
-51 + -25x + 6x2 = 50 + 25x + -50 + -25x

Reorder the terms:
-51 + -25x + 6x2 = 50 + -50 + 25x + -25x

Combine like terms: 50 + -50 = 0
-51 + -25x + 6x2 = 0 + 25x + -25x
-51 + -25x + 6x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
-51 + -25x + 6x2 = 0

Factor a trinomial.
(-3 + -2x)(17 + -3x) = 0


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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(17 + -3x)' equal to zero and attempt to solve:

Simplifying
17 + -3x = 0

Solving
17 + -3x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -3x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3x = 0 + -17
-3x = 0 + -17

Combine like terms: 0 + -17 = -17
-3x = -17

Divide each side by '-3'.
x = 5.666666667

Simplifying
x = 5.666666667
Solution
x = {-1.5, 5.666666667}

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