(2x+6)(3x-5)=10

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Solution for (2x+6)(3x-5)=10 equation: 


Simplifying
(2x + 6)(3x + -5) = 10

Reorder the terms:
(6 + 2x)(3x + -5) = 10

Reorder the terms:
(6 + 2x)(-5 + 3x) = 10

Multiply (6 + 2x) * (-5 + 3x)
(6(-5 + 3x) + 2x * (-5 + 3x)) = 10
((-5 * 6 + 3x * 6) + 2x * (-5 + 3x)) = 10
((-30 + 18x) + 2x * (-5 + 3x)) = 10
(-30 + 18x + (-5 * 2x + 3x * 2x)) = 10
(-30 + 18x + (-10x + 6x2)) = 10

Combine like terms: 18x + -10x = 8x
(-30 + 8x + 6x2) = 10

Solving
-30 + 8x + 6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-30 + -10 + 8x + 6x2 = 10 + -10

Combine like terms: -30 + -10 = -40
-40 + 8x + 6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-40 + 8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 4x + 3x2) = 0

Factor a trinomial.
2((-10 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, 2}

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