(x-4)(2x+3)=76

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Solution for (x-4)(2x+3)=76 equation: 


Simplifying
(x + -4)(2x + 3) = 76

Reorder the terms:
(-4 + x)(2x + 3) = 76

Reorder the terms:
(-4 + x)(3 + 2x) = 76

Multiply (-4 + x) * (3 + 2x)
(-4(3 + 2x) + x(3 + 2x)) = 76
((3 * -4 + 2x * -4) + x(3 + 2x)) = 76
((-12 + -8x) + x(3 + 2x)) = 76
(-12 + -8x + (3 * x + 2x * x)) = 76
(-12 + -8x + (3x + 2x2)) = 76

Combine like terms: -8x + 3x = -5x
(-12 + -5x + 2x2) = 76

Solving
-12 + -5x + 2x2 = 76

Solving for variable 'x'.

Reorder the terms:
-12 + -76 + -5x + 2x2 = 76 + -76

Combine like terms: -12 + -76 = -88
-88 + -5x + 2x2 = 76 + -76

Combine like terms: 76 + -76 = 0
-88 + -5x + 2x2 = 0

Factor a trinomial.
(-11 + -2x)(8 + -1x) = 0


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

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 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 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5

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 = {-5.5, 8}

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