(4x+8)(6x-5)=180

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Solution for (4x+8)(6x-5)=180 equation: 


Simplifying
(4x + 8)(6x + -5) = 180

Reorder the terms:
(8 + 4x)(6x + -5) = 180

Reorder the terms:
(8 + 4x)(-5 + 6x) = 180

Multiply (8 + 4x) * (-5 + 6x)
(8(-5 + 6x) + 4x * (-5 + 6x)) = 180
((-5 * 8 + 6x * 8) + 4x * (-5 + 6x)) = 180
((-40 + 48x) + 4x * (-5 + 6x)) = 180
(-40 + 48x + (-5 * 4x + 6x * 4x)) = 180
(-40 + 48x + (-20x + 24x2)) = 180

Combine like terms: 48x + -20x = 28x
(-40 + 28x + 24x2) = 180

Solving
-40 + 28x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
-40 + -180 + 28x + 24x2 = 180 + -180

Combine like terms: -40 + -180 = -220
-220 + 28x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-220 + 28x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-55 + 7x + 6x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 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 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-3.666666667, 2.5}

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