0=(4x^2)+7x-2

Solution for 0=(4x^2)+7x-2 equation:

Simplifying
0 = (4x2) + 7x + -2

Reorder the terms:
0 = -2 + 7x + (4x2)

Solving
0 = -2 + 7x + (4x2)

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -7x + (-4x2) = -2 + 7x + (4x2) + 2 + -7x + (-4x2)

Reorder the terms:
2 + -7x + (-4x2) = -2 + 2 + 7x + -7x + (4x2) + (-4x2)

Combine like terms: -2 + 2 = 0
2 + -7x + (-4x2) = 0 + 7x + -7x + (4x2) + (-4x2)
2 + -7x + (-4x2) = 7x + -7x + (4x2) + (-4x2)

Combine like terms: 7x + -7x = 0
2 + -7x + (-4x2) = 0 + (4x2) + (-4x2)
2 + -7x + (-4x2) = (4x2) + (-4x2)

Combine like terms: (4x2) + (-4x2) = 0
2 + -7x + (-4x2) = 0

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

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0.25, -2}