(3x-1)(2x+5)=-4x^2-2

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Solution for (3x-1)(2x+5)=-4x^2-2 equation: 


Simplifying
(3x + -1)(2x + 5) = -4x2 + -2

Reorder the terms:
(-1 + 3x)(2x + 5) = -4x2 + -2

Reorder the terms:
(-1 + 3x)(5 + 2x) = -4x2 + -2

Multiply (-1 + 3x) * (5 + 2x)
(-1(5 + 2x) + 3x * (5 + 2x)) = -4x2 + -2
((5 * -1 + 2x * -1) + 3x * (5 + 2x)) = -4x2 + -2
((-5 + -2x) + 3x * (5 + 2x)) = -4x2 + -2
(-5 + -2x + (5 * 3x + 2x * 3x)) = -4x2 + -2
(-5 + -2x + (15x + 6x2)) = -4x2 + -2

Combine like terms: -2x + 15x = 13x
(-5 + 13x + 6x2) = -4x2 + -2

Reorder the terms:
-5 + 13x + 6x2 = -2 + -4x2

Solving
-5 + 13x + 6x2 = -2 + -4x2

Solving for variable 'x'.

Reorder the terms:
-5 + 2 + 13x + 6x2 + 4x2 = -2 + -4x2 + 2 + 4x2

Combine like terms: -5 + 2 = -3
-3 + 13x + 6x2 + 4x2 = -2 + -4x2 + 2 + 4x2

Combine like terms: 6x2 + 4x2 = 10x2
-3 + 13x + 10x2 = -2 + -4x2 + 2 + 4x2

Reorder the terms:
-3 + 13x + 10x2 = -2 + 2 + -4x2 + 4x2

Combine like terms: -2 + 2 = 0
-3 + 13x + 10x2 = 0 + -4x2 + 4x2
-3 + 13x + 10x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-3 + 13x + 10x2 = 0

Factor a trinomial.
(-3 + -2x)(1 + -5x) = 0


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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-1.5, 0.2}

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