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

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


Simplifying
(5x + -2)(6x + 3) = 0

Reorder the terms:
(-2 + 5x)(6x + 3) = 0

Reorder the terms:
(-2 + 5x)(3 + 6x) = 0

Multiply (-2 + 5x) * (3 + 6x)
(-2(3 + 6x) + 5x * (3 + 6x)) = 0
((3 * -2 + 6x * -2) + 5x * (3 + 6x)) = 0
((-6 + -12x) + 5x * (3 + 6x)) = 0
(-6 + -12x + (3 * 5x + 6x * 5x)) = 0
(-6 + -12x + (15x + 30x2)) = 0

Combine like terms: -12x + 15x = 3x
(-6 + 3x + 30x2) = 0

Solving
-6 + 3x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + x + 10x2) = 0

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

Ignore the factor 3.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.5, 0.4}

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