(2x+5)(-3x+1)=19

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Solution for (2x+5)(-3x+1)=19 equation: 


Simplifying
(2x + 5)(-3x + 1) = 19

Reorder the terms:
(5 + 2x)(-3x + 1) = 19

Reorder the terms:
(5 + 2x)(1 + -3x) = 19

Multiply (5 + 2x) * (1 + -3x)
(5(1 + -3x) + 2x * (1 + -3x)) = 19
((1 * 5 + -3x * 5) + 2x * (1 + -3x)) = 19
((5 + -15x) + 2x * (1 + -3x)) = 19
(5 + -15x + (1 * 2x + -3x * 2x)) = 19
(5 + -15x + (2x + -6x2)) = 19

Combine like terms: -15x + 2x = -13x
(5 + -13x + -6x2) = 19

Solving
5 + -13x + -6x2 = 19

Solving for variable 'x'.

Reorder the terms:
5 + -19 + -13x + -6x2 = 19 + -19

Combine like terms: 5 + -19 = -14
-14 + -13x + -6x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-14 + -13x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 13x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + 13x + 6x2)' equal to zero and attempt to solve:

Simplifying
14 + 13x + 6x2 = 0

Solving
14 + 13x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
2.333333333 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 2.166666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 2.166666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + -2.333333333
2.166666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
2.166666667x + x2 = -2.333333333

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = -2.333333333 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = -2.333333333 + 1.173611113

Combine like terms: -2.333333333 + 1.173611113 = -1.15972222
1.173611113 + 2.166666667x + x2 = -1.15972222

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = -1.15972222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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