(7x-8)(5x+4)=4071

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Solution for (7x-8)(5x+4)=4071 equation: 


Simplifying
(7x + -8)(5x + 4) = 4071

Reorder the terms:
(-8 + 7x)(5x + 4) = 4071

Reorder the terms:
(-8 + 7x)(4 + 5x) = 4071

Multiply (-8 + 7x) * (4 + 5x)
(-8(4 + 5x) + 7x * (4 + 5x)) = 4071
((4 * -8 + 5x * -8) + 7x * (4 + 5x)) = 4071
((-32 + -40x) + 7x * (4 + 5x)) = 4071
(-32 + -40x + (4 * 7x + 5x * 7x)) = 4071
(-32 + -40x + (28x + 35x2)) = 4071

Combine like terms: -40x + 28x = -12x
(-32 + -12x + 35x2) = 4071

Solving
-32 + -12x + 35x2 = 4071

Solving for variable 'x'.

Reorder the terms:
-32 + -4071 + -12x + 35x2 = 4071 + -4071

Combine like terms: -32 + -4071 = -4103
-4103 + -12x + 35x2 = 4071 + -4071

Combine like terms: 4071 + -4071 = 0
-4103 + -12x + 35x2 = 0

Factor a trinomial.
(-373 + -35x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-373 + -35x)' equal to zero and attempt to solve:

Simplifying
-373 + -35x = 0

Solving
-373 + -35x = 0

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

Add '373' to each side of the equation.
-373 + 373 + -35x = 0 + 373

Combine like terms: -373 + 373 = 0
0 + -35x = 0 + 373
-35x = 0 + 373

Combine like terms: 0 + 373 = 373
-35x = 373

Divide each side by '-35'.
x = -10.65714286

Simplifying
x = -10.65714286

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 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 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-10.65714286, 11}

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