(2x+1)(3x-1)=25

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Solution for (2x+1)(3x-1)=25 equation: 


Simplifying
(2x + 1)(3x + -1) = 25

Reorder the terms:
(1 + 2x)(3x + -1) = 25

Reorder the terms:
(1 + 2x)(-1 + 3x) = 25

Multiply (1 + 2x) * (-1 + 3x)
(1(-1 + 3x) + 2x * (-1 + 3x)) = 25
((-1 * 1 + 3x * 1) + 2x * (-1 + 3x)) = 25
((-1 + 3x) + 2x * (-1 + 3x)) = 25
(-1 + 3x + (-1 * 2x + 3x * 2x)) = 25
(-1 + 3x + (-2x + 6x2)) = 25

Combine like terms: 3x + -2x = 1x
(-1 + 1x + 6x2) = 25

Solving
-1 + 1x + 6x2 = 25

Solving for variable 'x'.

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

Combine like terms: -1 + -25 = -26
-26 + 1x + 6x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-26 + 1x + 6x2 = 0

Factor a trinomial.
(-13 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -6x)' equal to zero and attempt to solve:

Simplifying
-13 + -6x = 0

Solving
-13 + -6x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6x = 0 + 13
-6x = 0 + 13

Combine like terms: 0 + 13 = 13
-6x = 13

Divide each side by '-6'.
x = -2.166666667

Simplifying
x = -2.166666667

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 = {-2.166666667, 2}

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