(10x-4)(2x+3)=0

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Solution for (10x-4)(2x+3)=0 equation: 


Simplifying
(10x + -4)(2x + 3) = 0

Reorder the terms:
(-4 + 10x)(2x + 3) = 0

Reorder the terms:
(-4 + 10x)(3 + 2x) = 0

Multiply (-4 + 10x) * (3 + 2x)
(-4(3 + 2x) + 10x * (3 + 2x)) = 0
((3 * -4 + 2x * -4) + 10x * (3 + 2x)) = 0
((-12 + -8x) + 10x * (3 + 2x)) = 0
(-12 + -8x + (3 * 10x + 2x * 10x)) = 0
(-12 + -8x + (30x + 20x2)) = 0

Combine like terms: -8x + 30x = 22x
(-12 + 22x + 20x2) = 0

Solving
-12 + 22x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11x + 10x2) = 0

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

Ignore the factor 2.

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 '(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 = {-1.5, 0.4}

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