4(2x+3)(5x-11)=0

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Solution for 4(2x+3)(5x-11)=0 equation: 


Simplifying
4(2x + 3)(5x + -11) = 0

Reorder the terms:
4(3 + 2x)(5x + -11) = 0

Reorder the terms:
4(3 + 2x)(-11 + 5x) = 0

Multiply (3 + 2x) * (-11 + 5x)
4(3(-11 + 5x) + 2x * (-11 + 5x)) = 0
4((-11 * 3 + 5x * 3) + 2x * (-11 + 5x)) = 0
4((-33 + 15x) + 2x * (-11 + 5x)) = 0
4(-33 + 15x + (-11 * 2x + 5x * 2x)) = 0
4(-33 + 15x + (-22x + 10x2)) = 0

Combine like terms: 15x + -22x = -7x
4(-33 + -7x + 10x2) = 0
(-33 * 4 + -7x * 4 + 10x2 * 4) = 0
(-132 + -28x + 40x2) = 0

Solving
-132 + -28x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-33 + -7x + 10x2) = 0

Factor a trinomial.
4((-3 + -2x)(11 + -5x)) = 0

Ignore the factor 4.

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 '(11 + -5x)' equal to zero and attempt to solve:

Simplifying
11 + -5x = 0

Solving
11 + -5x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x = 0 + -11
-5x = 0 + -11

Combine like terms: 0 + -11 = -11
-5x = -11

Divide each side by '-5'.
x = 2.2

Simplifying
x = 2.2
Solution
x = {-1.5, 2.2}

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