(3x-2)(x+5)=14x-8

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Solution for (3x-2)(x+5)=14x-8 equation:


Simplifying
(3x + -2)(x + 5) = 14x + -8

Reorder the terms:
(-2 + 3x)(x + 5) = 14x + -8

Reorder the terms:
(-2 + 3x)(5 + x) = 14x + -8

Multiply (-2 + 3x) * (5 + x)
(-2(5 + x) + 3x * (5 + x)) = 14x + -8
((5 * -2 + x * -2) + 3x * (5 + x)) = 14x + -8
((-10 + -2x) + 3x * (5 + x)) = 14x + -8
(-10 + -2x + (5 * 3x + x * 3x)) = 14x + -8
(-10 + -2x + (15x + 3x2)) = 14x + -8

Combine like terms: -2x + 15x = 13x
(-10 + 13x + 3x2) = 14x + -8

Reorder the terms:
-10 + 13x + 3x2 = -8 + 14x

Solving
-10 + 13x + 3x2 = -8 + 14x

Solving for variable 'x'.

Reorder the terms:
-10 + 8 + 13x + -14x + 3x2 = -8 + 14x + 8 + -14x

Combine like terms: -10 + 8 = -2
-2 + 13x + -14x + 3x2 = -8 + 14x + 8 + -14x

Combine like terms: 13x + -14x = -1x
-2 + -1x + 3x2 = -8 + 14x + 8 + -14x

Reorder the terms:
-2 + -1x + 3x2 = -8 + 8 + 14x + -14x

Combine like terms: -8 + 8 = 0
-2 + -1x + 3x2 = 0 + 14x + -14x
-2 + -1x + 3x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-2 + -1x + 3x2 = 0

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


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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, 1}

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