(x+9)(4x-5)=31x-36

Solution for (x+9)(4x-5)=31x-36 equation:

Simplifying
(x + 9)(4x + -5) = 31x + -36

Reorder the terms:
(9 + x)(4x + -5) = 31x + -36

Reorder the terms:
(9 + x)(-5 + 4x) = 31x + -36

Multiply (9 + x) * (-5 + 4x)
(9(-5 + 4x) + x(-5 + 4x)) = 31x + -36
((-5 * 9 + 4x * 9) + x(-5 + 4x)) = 31x + -36
((-45 + 36x) + x(-5 + 4x)) = 31x + -36
(-45 + 36x + (-5 * x + 4x * x)) = 31x + -36
(-45 + 36x + (-5x + 4x2)) = 31x + -36

Combine like terms: 36x + -5x = 31x
(-45 + 31x + 4x2) = 31x + -36

Reorder the terms:
-45 + 31x + 4x2 = -36 + 31x

Add '-31x' to each side of the equation.
-45 + 31x + -31x + 4x2 = -36 + 31x + -31x

Combine like terms: 31x + -31x = 0
-45 + 0 + 4x2 = -36 + 31x + -31x
-45 + 4x2 = -36 + 31x + -31x

Combine like terms: 31x + -31x = 0
-45 + 4x2 = -36 + 0
-45 + 4x2 = -36

Solving
-45 + 4x2 = -36

Solving for variable 'x'.

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

Add '45' to each side of the equation.
-45 + 45 + 4x2 = -36 + 45

Combine like terms: -45 + 45 = 0
0 + 4x2 = -36 + 45
4x2 = -36 + 45

Combine like terms: -36 + 45 = 9
4x2 = 9

Divide each side by '4'.
x2 = 2.25

Simplifying
x2 = 2.25

Take the square root of each side:
x = {-1.5, 1.5}