150-(8x+5)(x+1)=34

Solution for 150-(8x+5)(x+1)=34 equation:

Simplifying
150 + -1(8x + 5)(x + 1) = 34

Reorder the terms:
150 + -1(5 + 8x)(x + 1) = 34

Reorder the terms:
150 + -1(5 + 8x)(1 + x) = 34

Multiply (5 + 8x) * (1 + x)
150 + -1(5(1 + x) + 8x * (1 + x)) = 34
150 + -1((1 * 5 + x * 5) + 8x * (1 + x)) = 34
150 + -1((5 + 5x) + 8x * (1 + x)) = 34
150 + -1(5 + 5x + (1 * 8x + x * 8x)) = 34
150 + -1(5 + 5x + (8x + 8x2)) = 34

Combine like terms: 5x + 8x = 13x
150 + -1(5 + 13x + 8x2) = 34
150 + (5 * -1 + 13x * -1 + 8x2 * -1) = 34
150 + (-5 + -13x + -8x2) = 34

Combine like terms: 150 + -5 = 145
145 + -13x + -8x2 = 34

Solving
145 + -13x + -8x2 = 34

Solving for variable 'x'.

Reorder the terms:
145 + -34 + -13x + -8x2 = 34 + -34

Combine like terms: 145 + -34 = 111
111 + -13x + -8x2 = 34 + -34

Combine like terms: 34 + -34 = 0
111 + -13x + -8x2 = 0

Factor a trinomial.
(3 + -1x)(37 + 8x) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(37 + 8x)' equal to zero and attempt to solve:

Simplifying
37 + 8x = 0

Solving
37 + 8x = 0

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

Add '-37' to each side of the equation.
37 + -37 + 8x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 8x = 0 + -37
8x = 0 + -37

Combine like terms: 0 + -37 = -37
8x = -37

Divide each side by '8'.
x = -4.625

Simplifying
x = -4.625
Solution
x = {3, -4.625}