4x(x+10)=-7x+65

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Solution for 4x(x+10)=-7x+65 equation:


Simplifying
4x(x + 10) = -7x + 65

Reorder the terms:
4x(10 + x) = -7x + 65
(10 * 4x + x * 4x) = -7x + 65
(40x + 4x2) = -7x + 65

Reorder the terms:
40x + 4x2 = 65 + -7x

Solving
40x + 4x2 = 65 + -7x

Solving for variable 'x'.

Reorder the terms:
-65 + 40x + 7x + 4x2 = 65 + -7x + -65 + 7x

Combine like terms: 40x + 7x = 47x
-65 + 47x + 4x2 = 65 + -7x + -65 + 7x

Reorder the terms:
-65 + 47x + 4x2 = 65 + -65 + -7x + 7x

Combine like terms: 65 + -65 = 0
-65 + 47x + 4x2 = 0 + -7x + 7x
-65 + 47x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-65 + 47x + 4x2 = 0

Factor a trinomial.
(-13 + -1x)(5 + -4x) = 0


Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13

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

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

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

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

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

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-13, 1.25}

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