4(2+3x)(x-5)=0

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Solution for 4(2+3x)(x-5)=0 equation: 


Simplifying
4(2 + 3x)(x + -5) = 0

Reorder the terms:
4(2 + 3x)(-5 + x) = 0

Multiply (2 + 3x) * (-5 + x)
4(2(-5 + x) + 3x * (-5 + x)) = 0
4((-5 * 2 + x * 2) + 3x * (-5 + x)) = 0
4((-10 + 2x) + 3x * (-5 + x)) = 0
4(-10 + 2x + (-5 * 3x + x * 3x)) = 0
4(-10 + 2x + (-15x + 3x2)) = 0

Combine like terms: 2x + -15x = -13x
4(-10 + -13x + 3x2) = 0
(-10 * 4 + -13x * 4 + 3x2 * 4) = 0
(-40 + -52x + 12x2) = 0

Solving
-40 + -52x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -13x + 3x2) = 0

Factor a trinomial.
4((-2 + -3x)(5 + -1x)) = 0

Ignore the factor 4.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.6666666667, 5}

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