(x-2)(4x+7)=-11

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Solution for (x-2)(4x+7)=-11 equation: 


Simplifying
(x + -2)(4x + 7) = -11

Reorder the terms:
(-2 + x)(4x + 7) = -11

Reorder the terms:
(-2 + x)(7 + 4x) = -11

Multiply (-2 + x) * (7 + 4x)
(-2(7 + 4x) + x(7 + 4x)) = -11
((7 * -2 + 4x * -2) + x(7 + 4x)) = -11
((-14 + -8x) + x(7 + 4x)) = -11
(-14 + -8x + (7 * x + 4x * x)) = -11
(-14 + -8x + (7x + 4x2)) = -11

Combine like terms: -8x + 7x = -1x
(-14 + -1x + 4x2) = -11

Solving
-14 + -1x + 4x2 = -11

Solving for variable 'x'.

Reorder the terms:
-14 + 11 + -1x + 4x2 = -11 + 11

Combine like terms: -14 + 11 = -3
-3 + -1x + 4x2 = -11 + 11

Combine like terms: -11 + 11 = 0
-3 + -1x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.75, 1}

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