10x^2=7x+3

Solution for 10x^2=7x+3 equation:

Simplifying
10x2 = 7x + 3

Reorder the terms:
10x2 = 3 + 7x

Solving
10x2 = 3 + 7x

Solving for variable 'x'.

Reorder the terms:
-3 + -7x + 10x2 = 3 + 7x + -3 + -7x

Reorder the terms:
-3 + -7x + 10x2 = 3 + -3 + 7x + -7x

Combine like terms: 3 + -3 = 0
-3 + -7x + 10x2 = 0 + 7x + -7x
-3 + -7x + 10x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-3 + -7x + 10x2 = 0

Factor a trinomial.
(-3 + -10x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -10x)' equal to zero and attempt to solve:

Simplifying
-3 + -10x = 0

Solving
-3 + -10x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -10x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10x = 0 + 3
-10x = 0 + 3

Combine like terms: 0 + 3 = 3
-10x = 3

Divide each side by '-10'.
x = -0.3

Simplifying
x = -0.3
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 = {-0.3, 1}