4x^2-14x=18

Solution for 4x^2-14x=18 equation:

Simplifying
4x2 + -14x = 18

Reorder the terms:
-14x + 4x2 = 18

Solving
-14x + 4x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + -14x + 4x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -7x + 2x2) = 0

Factor a trinomial.
2((-1 + -1x)(9 + -2x)) = 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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-1, 4.5}