2x(x-7)+5(x-7)=0

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Solution for 2x(x-7)+5(x-7)=0 equation: 


Simplifying
2x(x + -7) + 5(x + -7) = 0

Reorder the terms:
2x(-7 + x) + 5(x + -7) = 0
(-7 * 2x + x * 2x) + 5(x + -7) = 0
(-14x + 2x2) + 5(x + -7) = 0

Reorder the terms:
-14x + 2x2 + 5(-7 + x) = 0
-14x + 2x2 + (-7 * 5 + x * 5) = 0
-14x + 2x2 + (-35 + 5x) = 0

Reorder the terms:
-35 + -14x + 5x + 2x2 = 0

Combine like terms: -14x + 5x = -9x
-35 + -9x + 2x2 = 0

Solving
-35 + -9x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2.5, 7}

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