2(x^2-5)-7x=4x-22

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Solution for 2(x^2-5)-7x=4x-22 equation: 


Simplifying
2(x2 + -5) + -7x = 4x + -22

Reorder the terms:
2(-5 + x2) + -7x = 4x + -22
(-5 * 2 + x2 * 2) + -7x = 4x + -22
(-10 + 2x2) + -7x = 4x + -22

Reorder the terms:
-10 + -7x + 2x2 = 4x + -22

Reorder the terms:
-10 + -7x + 2x2 = -22 + 4x

Solving
-10 + -7x + 2x2 = -22 + 4x

Solving for variable 'x'.

Reorder the terms:
-10 + 22 + -7x + -4x + 2x2 = -22 + 4x + 22 + -4x

Combine like terms: -10 + 22 = 12
12 + -7x + -4x + 2x2 = -22 + 4x + 22 + -4x

Combine like terms: -7x + -4x = -11x
12 + -11x + 2x2 = -22 + 4x + 22 + -4x

Reorder the terms:
12 + -11x + 2x2 = -22 + 22 + 4x + -4x

Combine like terms: -22 + 22 = 0
12 + -11x + 2x2 = 0 + 4x + -4x
12 + -11x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
12 + -11x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1.5, 4}

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