(7x-5)(6x+8)=180

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Solution for (7x-5)(6x+8)=180 equation: 


Simplifying
(7x + -5)(6x + 8) = 180

Reorder the terms:
(-5 + 7x)(6x + 8) = 180

Reorder the terms:
(-5 + 7x)(8 + 6x) = 180

Multiply (-5 + 7x) * (8 + 6x)
(-5(8 + 6x) + 7x * (8 + 6x)) = 180
((8 * -5 + 6x * -5) + 7x * (8 + 6x)) = 180
((-40 + -30x) + 7x * (8 + 6x)) = 180
(-40 + -30x + (8 * 7x + 6x * 7x)) = 180
(-40 + -30x + (56x + 42x2)) = 180

Combine like terms: -30x + 56x = 26x
(-40 + 26x + 42x2) = 180

Solving
-40 + 26x + 42x2 = 180

Solving for variable 'x'.

Reorder the terms:
-40 + -180 + 26x + 42x2 = 180 + -180

Combine like terms: -40 + -180 = -220
-220 + 26x + 42x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-220 + 26x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-110 + 13x + 21x2) = 0

Factor a trinomial.
2((-55 + -21x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + -21x)' equal to zero and attempt to solve:

Simplifying
-55 + -21x = 0

Solving
-55 + -21x = 0

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

Add '55' to each side of the equation.
-55 + 55 + -21x = 0 + 55

Combine like terms: -55 + 55 = 0
0 + -21x = 0 + 55
-21x = 0 + 55

Combine like terms: 0 + 55 = 55
-21x = 55

Divide each side by '-21'.
x = -2.619047619

Simplifying
x = -2.619047619

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.619047619, 2}

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