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

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


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

Reorder the terms:
7x(-7 + x) = (2x + 5)(x + -7)
(-7 * 7x + x * 7x) = (2x + 5)(x + -7)
(-49x + 7x2) = (2x + 5)(x + -7)

Reorder the terms:
-49x + 7x2 = (5 + 2x)(x + -7)

Reorder the terms:
-49x + 7x2 = (5 + 2x)(-7 + x)

Multiply (5 + 2x) * (-7 + x)
-49x + 7x2 = (5(-7 + x) + 2x * (-7 + x))
-49x + 7x2 = ((-7 * 5 + x * 5) + 2x * (-7 + x))
-49x + 7x2 = ((-35 + 5x) + 2x * (-7 + x))
-49x + 7x2 = (-35 + 5x + (-7 * 2x + x * 2x))
-49x + 7x2 = (-35 + 5x + (-14x + 2x2))

Combine like terms: 5x + -14x = -9x
-49x + 7x2 = (-35 + -9x + 2x2)

Solving
-49x + 7x2 = -35 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
35 + -49x + 9x + 7x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Combine like terms: -49x + 9x = -40x
35 + -40x + 7x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
35 + -40x + 5x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2

Reorder the terms:
35 + -40x + 5x2 = -35 + 35 + -9x + 9x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
35 + -40x + 5x2 = 0 + -9x + 9x + 2x2 + -2x2
35 + -40x + 5x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
35 + -40x + 5x2 = 0 + 2x2 + -2x2
35 + -40x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
35 + -40x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -8x + x2) = 0

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

Ignore the factor 5.

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 '(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 = {1, 7}

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