3x^2-3+(2x+5)(x-1)=0

Solution for 3x^2-3+(2x+5)(x-1)=0 equation:

Simplifying
3x2 + -3 + (2x + 5)(x + -1) = 0

Reorder the terms:
3x2 + -3 + (5 + 2x)(x + -1) = 0

Reorder the terms:
3x2 + -3 + (5 + 2x)(-1 + x) = 0

Multiply (5 + 2x) * (-1 + x)
3x2 + -3 + (5(-1 + x) + 2x * (-1 + x)) = 0
3x2 + -3 + ((-1 * 5 + x * 5) + 2x * (-1 + x)) = 0
3x2 + -3 + ((-5 + 5x) + 2x * (-1 + x)) = 0
3x2 + -3 + (-5 + 5x + (-1 * 2x + x * 2x)) = 0
3x2 + -3 + (-5 + 5x + (-2x + 2x2)) = 0

Combine like terms: 5x + -2x = 3x
3x2 + -3 + (-5 + 3x + 2x2) = 0

Reorder the terms:
-3 + -5 + 3x + 3x2 + 2x2 = 0

Combine like terms: -3 + -5 = -8
-8 + 3x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
-8 + 3x + 5x2 = 0

Solving
-8 + 3x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -5x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 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 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6
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 = {-1.6, 1}