(2x+7)(x-4)=92

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Solution for (2x+7)(x-4)=92 equation: 


Simplifying
(2x + 7)(x + -4) = 92

Reorder the terms:
(7 + 2x)(x + -4) = 92

Reorder the terms:
(7 + 2x)(-4 + x) = 92

Multiply (7 + 2x) * (-4 + x)
(7(-4 + x) + 2x * (-4 + x)) = 92
((-4 * 7 + x * 7) + 2x * (-4 + x)) = 92
((-28 + 7x) + 2x * (-4 + x)) = 92
(-28 + 7x + (-4 * 2x + x * 2x)) = 92
(-28 + 7x + (-8x + 2x2)) = 92

Combine like terms: 7x + -8x = -1x
(-28 + -1x + 2x2) = 92

Solving
-28 + -1x + 2x2 = 92

Solving for variable 'x'.

Reorder the terms:
-28 + -92 + -1x + 2x2 = 92 + -92

Combine like terms: -28 + -92 = -120
-120 + -1x + 2x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-120 + -1x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-7.5, 8}

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