(5x-4)*(2x+3)=5

Solution for (5x-4)*(2x+3)=5 equation:

Simplifying
(5x + -4)(2x + 3) = 5

Reorder the terms:
(-4 + 5x)(2x + 3) = 5

Reorder the terms:
(-4 + 5x)(3 + 2x) = 5

Multiply (-4 + 5x) * (3 + 2x)
(-4(3 + 2x) + 5x * (3 + 2x)) = 5
((3 * -4 + 2x * -4) + 5x * (3 + 2x)) = 5
((-12 + -8x) + 5x * (3 + 2x)) = 5
(-12 + -8x + (3 * 5x + 2x * 5x)) = 5
(-12 + -8x + (15x + 10x2)) = 5

Combine like terms: -8x + 15x = 7x
(-12 + 7x + 10x2) = 5

Solving
-12 + 7x + 10x2 = 5

Solving for variable 'x'.

Reorder the terms:
-12 + -5 + 7x + 10x2 = 5 + -5

Combine like terms: -12 + -5 = -17
-17 + 7x + 10x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-17 + 7x + 10x2 = 0

Factor a trinomial.
(-17 + -10x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -10x)' equal to zero and attempt to solve:

Simplifying
-17 + -10x = 0

Solving
-17 + -10x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -10x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -10x = 0 + 17
-10x = 0 + 17

Combine like terms: 0 + 17 = 17
-10x = 17

Divide each side by '-10'.
x = -1.7

Simplifying
x = -1.7
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 = {-1.7, 1}