140x^2=182x-56

Solution for 140x^2=182x-56 equation:

Simplifying
140x2 = 182x + -56

Reorder the terms:
140x2 = -56 + 182x

Solving
140x2 = -56 + 182x

Solving for variable 'x'.

Reorder the terms:
56 + -182x + 140x2 = -56 + 182x + 56 + -182x

Reorder the terms:
56 + -182x + 140x2 = -56 + 56 + 182x + -182x

Combine like terms: -56 + 56 = 0
56 + -182x + 140x2 = 0 + 182x + -182x
56 + -182x + 140x2 = 182x + -182x

Combine like terms: 182x + -182x = 0
56 + -182x + 140x2 = 0

Factor out the Greatest Common Factor (GCF), '14'.
14(4 + -13x + 10x2) = 0

Factor a trinomial.
14((1 + -2x)(4 + -5x)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {0.5, 0.8}