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

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


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

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

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

Multiply (2 + x) * (5 + -3x)
4(2(5 + -3x) + x(5 + -3x)) = 0
4((5 * 2 + -3x * 2) + x(5 + -3x)) = 0
4((10 + -6x) + x(5 + -3x)) = 0
4(10 + -6x + (5 * x + -3x * x)) = 0
4(10 + -6x + (5x + -3x2)) = 0

Combine like terms: -6x + 5x = -1x
4(10 + -1x + -3x2) = 0
(10 * 4 + -1x * 4 + -3x2 * 4) = 0
(40 + -4x + -12x2) = 0

Solving
40 + -4x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -1x + -3x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {1.666666667, -2}

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