8x^2+(x+1)(6x+15)-50=0

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Solution for 8x^2+(x+1)(6x+15)-50=0 equation: 


Simplifying
8x2 + (x + 1)(6x + 15) + -50 = 0

Reorder the terms:
8x2 + (1 + x)(6x + 15) + -50 = 0

Reorder the terms:
8x2 + (1 + x)(15 + 6x) + -50 = 0

Multiply (1 + x) * (15 + 6x)
8x2 + (1(15 + 6x) + x(15 + 6x)) + -50 = 0
8x2 + ((15 * 1 + 6x * 1) + x(15 + 6x)) + -50 = 0
8x2 + ((15 + 6x) + x(15 + 6x)) + -50 = 0
8x2 + (15 + 6x + (15 * x + 6x * x)) + -50 = 0
8x2 + (15 + 6x + (15x + 6x2)) + -50 = 0

Combine like terms: 6x + 15x = 21x
8x2 + (15 + 21x + 6x2) + -50 = 0

Reorder the terms:
15 + -50 + 21x + 8x2 + 6x2 = 0

Combine like terms: 15 + -50 = -35
-35 + 21x + 8x2 + 6x2 = 0

Combine like terms: 8x2 + 6x2 = 14x2
-35 + 21x + 14x2 = 0

Solving
-35 + 21x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + 3x + 2x2) = 0

Factor a trinomial.
7((-5 + -2x)(1 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.5, 1}

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