2x*x-3=4x-5

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

Simplifying
2x * x + -3 = 4x + -5

Multiply x * x
2x2 + -3 = 4x + -5

Reorder the terms:
-3 + 2x2 = 4x + -5

Reorder the terms:
-3 + 2x2 = -5 + 4x

Solving
-3 + 2x2 = -5 + 4x

Solving for variable 'x'.

Reorder the terms:
-3 + 5 + -4x + 2x2 = -5 + 4x + 5 + -4x

Combine like terms: -3 + 5 = 2
2 + -4x + 2x2 = -5 + 4x + 5 + -4x

Reorder the terms:
2 + -4x + 2x2 = -5 + 5 + 4x + -4x

Combine like terms: -5 + 5 = 0
2 + -4x + 2x2 = 0 + 4x + -4x
2 + -4x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
2 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2x + x2) = 0

Factor a trinomial.
2((1 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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, 1}