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

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


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

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

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

Multiply (2 + 4x) * (-10 + 3x)
(2(-10 + 3x) + 4x * (-10 + 3x)) = 0
((-10 * 2 + 3x * 2) + 4x * (-10 + 3x)) = 0
((-20 + 6x) + 4x * (-10 + 3x)) = 0
(-20 + 6x + (-10 * 4x + 3x * 4x)) = 0
(-20 + 6x + (-40x + 12x2)) = 0

Combine like terms: 6x + -40x = -34x
(-20 + -34x + 12x2) = 0

Solving
-20 + -34x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -17x + 6x2) = 0

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

Ignore the factor 2.

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 '(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
Solution
x = {-0.5, 3.333333333}

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