4(3x-5)(x+1)=0

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Solution for 4(3x-5)(x+1)=0 equation: 


Simplifying
4(3x + -5)(x + 1) = 0

Reorder the terms:
4(-5 + 3x)(x + 1) = 0

Reorder the terms:
4(-5 + 3x)(1 + x) = 0

Multiply (-5 + 3x) * (1 + x)
4(-5(1 + x) + 3x * (1 + x)) = 0
4((1 * -5 + x * -5) + 3x * (1 + x)) = 0
4((-5 + -5x) + 3x * (1 + x)) = 0
4(-5 + -5x + (1 * 3x + x * 3x)) = 0
4(-5 + -5x + (3x + 3x2)) = 0

Combine like terms: -5x + 3x = -2x
4(-5 + -2x + 3x2) = 0
(-5 * 4 + -2x * 4 + 3x2 * 4) = 0
(-20 + -8x + 12x2) = 0

Solving
-20 + -8x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -2x + 3x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, 1.666666667}

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